Electric motors (part 1)

WEBVTT
Kind: captions
Language: en

00:00:00.730 --> 00:00:03.590
Let's say we have a magnetic
field that's coming out of the

00:00:03.590 --> 00:00:04.920
right side of the screen.

00:00:04.920 --> 00:00:09.340
And it's not just along the
screen, it's actually three

00:00:09.340 --> 00:00:10.110
dimensional.

00:00:10.110 --> 00:00:13.470
So it's going above the
screen, below, but the

00:00:13.470 --> 00:00:15.550
direction of the magnetic
field is from the

00:00:15.550 --> 00:00:16.410
right to the left.

00:00:16.410 --> 00:00:17.760
Let me just draw that.

00:00:17.760 --> 00:00:20.790
And I'm not going to draw a
bunch of the field vector

00:00:20.790 --> 00:00:24.060
arrows because that'll just
take up a lot of valuable

00:00:24.060 --> 00:00:28.160
space on our-- so that's the
vector magnetic field.

00:00:28.160 --> 00:00:30.430
It's down here, too.

00:00:30.430 --> 00:00:34.390
If I could, I would draw it
above your screen and below

00:00:34.390 --> 00:00:34.780
your screen.

00:00:34.780 --> 00:00:36.630
But it's coming from the
right to the left.

00:00:36.630 --> 00:00:38.380
And then in that magnetic
field I

00:00:38.380 --> 00:00:41.390
have an electric circuit.

00:00:41.390 --> 00:00:42.750
I won't draw the whole
circuit right now.

00:00:42.750 --> 00:00:43.525
I'll do that in a second.

00:00:43.525 --> 00:00:46.410
But let's say I have--
part of the electric

00:00:46.410 --> 00:00:47.640
circuit is a loop.

00:00:47.640 --> 00:00:48.760
And the loop looks like this.

00:00:48.760 --> 00:00:50.990
I'm trying to draw
it carefully.

00:00:50.990 --> 00:00:53.820
So that we can-- because I think
a careful drawing will

00:00:53.820 --> 00:00:56.210
be more useful in
a second than an

00:00:56.210 --> 00:00:58.540
uncarefully drawn drawing.

00:00:58.540 --> 00:00:59.050
So let's see.

00:00:59.050 --> 00:01:00.540
So it's a loop.

00:01:00.540 --> 00:01:03.700
You can almost-- you could
imagine taking a paper clip

00:01:03.700 --> 00:01:05.670
and putting it into
this shape.

00:01:08.660 --> 00:01:12.700
Oh, that's good enough,
I think.

00:01:12.700 --> 00:01:15.250
And I have a current going
in this direction

00:01:15.250 --> 00:01:16.190
in this paper clip.

00:01:16.190 --> 00:01:18.630
So this is the positive,
that's the negative.

00:01:18.630 --> 00:01:20.210
So the current is
going like that.

00:01:23.130 --> 00:01:26.640
Current is going in
a loop like that.

00:01:26.640 --> 00:01:27.930
The current's coming out
of this end, it's

00:01:27.930 --> 00:01:30.260
coming into this end.

00:01:30.260 --> 00:01:34.420
And let's say that loop of--
it could be a paper clip or

00:01:34.420 --> 00:01:36.300
anything-- let's say
that it can rotate.

00:01:36.300 --> 00:01:36.980
And that's important.

00:01:36.980 --> 00:01:38.300
What's going to happen?

00:01:38.300 --> 00:01:41.590
Well, my magnetic field is
coming in this direction.

00:01:41.590 --> 00:01:45.600
The current is going
down here, up here.

00:01:45.600 --> 00:01:48.610
What's going to be the net
force of the magnetic

00:01:48.610 --> 00:01:50.600
field on this loop?

00:01:50.600 --> 00:01:51.980
Well, let's try it out.

00:01:51.980 --> 00:01:54.220
And it turns out it's going to
be a different magnitude at

00:01:54.220 --> 00:01:55.950
different points
of the current.

00:01:55.950 --> 00:01:57.140
So here.

00:01:57.140 --> 00:01:59.580
And we don't worry about-- all
we're worried about right now

00:01:59.580 --> 00:02:00.620
is direction.

00:02:00.620 --> 00:02:03.190
And then maybe a little
intuition of the magnitude.

00:02:03.190 --> 00:02:08.550
So we know that the force of the
magnetic field is equal to

00:02:08.550 --> 00:02:12.830
the current times the
length vector cross

00:02:12.830 --> 00:02:15.670
the magnetic field.

00:02:15.670 --> 00:02:20.390
Well, what would be the force of
the magnetic field on this

00:02:20.390 --> 00:02:21.480
segment of wire?

00:02:21.480 --> 00:02:24.110
We could call this L.

00:02:24.110 --> 00:02:27.766
And that L goes in the same
direction as the current.

00:02:27.766 --> 00:02:28.900
Well, let's see.

00:02:28.900 --> 00:02:31.390
Current is just a scalar,
but L is going down.

00:02:31.390 --> 00:02:32.720
Magnetic field going
to the left.

00:02:32.720 --> 00:02:34.000
Cross product.

00:02:34.000 --> 00:02:39.850
Cross product, I take my right
hand, put my index finger in

00:02:39.850 --> 00:02:45.390
the direction of the current,
or in the direction of L,

00:02:45.390 --> 00:02:46.980
because that's the first term
of the cross product.

00:02:46.980 --> 00:02:48.760
So that's the index finger.

00:02:48.760 --> 00:02:52.000
So my index finger goes down,
because that's the direction

00:02:52.000 --> 00:02:53.550
of the current.

00:02:53.550 --> 00:02:56.460
And then my middle finger-- and
remember, you have to do

00:02:56.460 --> 00:02:57.020
this with the right hand.

00:02:57.020 --> 00:02:58.120
If you do it with the left hand,
you're going to get the

00:02:58.120 --> 00:02:59.310
opposite result.

00:02:59.310 --> 00:03:01.400
And now my middle finger is
going to go in the direction

00:03:01.400 --> 00:03:01.940
of the field.

00:03:01.940 --> 00:03:06.250
So let me point my
middle finger.

00:03:06.250 --> 00:03:07.930
My middle finger is
going to go in the

00:03:07.930 --> 00:03:09.870
direction of the field.

00:03:09.870 --> 00:03:11.800
I keep having to look
at my own hand.

00:03:11.800 --> 00:03:13.900
And then my other two fingers
are just going to do what they

00:03:13.900 --> 00:03:15.400
need to do.

00:03:15.400 --> 00:03:16.780
So that's my third finger.

00:03:16.780 --> 00:03:19.740
That's my pinky.

00:03:19.740 --> 00:03:23.810
And then what is my
thumb going to do?

00:03:23.810 --> 00:03:25.240
What is my thumb going to do?

00:03:25.240 --> 00:03:30.020
Well, my hand-- that's
my hand.

00:03:30.020 --> 00:03:31.240
This is what my hand is doing.

00:03:31.240 --> 00:03:33.350
I'm pointing downward.

00:03:33.350 --> 00:03:36.710
And my palm is kind of
pointing at my body.

00:03:36.710 --> 00:03:39.360
So what is my thumb doing?

00:03:39.360 --> 00:03:40.320
I know it's hard to see.

00:03:40.320 --> 00:03:43.220
This is my middle finger
right here.

00:03:43.220 --> 00:03:45.290
So my thumb is on the other
side of this drawing.

00:03:45.290 --> 00:03:47.070
And my thumb is pointing
downwards.

00:03:47.070 --> 00:03:48.350
I hope you see that.

00:03:48.350 --> 00:03:50.120
And you try it with
your own hand.

00:03:50.120 --> 00:03:51.490
So my thumb is pointing
downwards.

00:03:51.490 --> 00:03:54.900
So the direction of the force
created by the magnetic field

00:03:54.900 --> 00:03:56.860
on this current is going
to go downward.

00:03:56.860 --> 00:03:58.380
So let me draw that.

00:03:58.380 --> 00:04:01.740
So the force vector--
I'll do it in this

00:04:01.740 --> 00:04:03.350
orangey brown color.

00:04:03.350 --> 00:04:07.650
The force vector on this segment
of the wire is going

00:04:07.650 --> 00:04:10.360
to be going down.

00:04:10.360 --> 00:04:12.660
Now what about this segment
of the wire?

00:04:12.660 --> 00:04:13.440
Well, think about it.

00:04:13.440 --> 00:04:23.040
This segment of the wire, the
L vector-- this L vector--

00:04:23.040 --> 00:04:24.920
It's parallel to the magnetic
field just in

00:04:24.920 --> 00:04:26.170
the opposite direction.

00:04:26.170 --> 00:04:29.040
And so when you take the cross
product-- remember, the cross

00:04:29.040 --> 00:04:31.590
product is you're multiplying
the magnitude of the vectors

00:04:31.590 --> 00:04:33.390
that are perpendicular
to each other.

00:04:33.390 --> 00:04:36.480
But if this is the L vector
right here, there's no

00:04:36.480 --> 00:04:38.260
component of it that it's
perpendicular to

00:04:38.260 --> 00:04:39.510
the magnetic field.

00:04:39.510 --> 00:04:44.050
So the magnetic field and the
current are in the same plane.

00:04:44.050 --> 00:04:45.250
They're parallel.

00:04:45.250 --> 00:04:46.450
They're not orthogonal at all.

00:04:46.450 --> 00:04:49.140
There's no components of them
that are at 90 degrees.

00:04:49.140 --> 00:04:51.130
So when you take the cross
product, you're going to see

00:04:51.130 --> 00:04:53.790
that the net force on this
segment of the wire is 0.

00:04:53.790 --> 00:04:55.840
And likewise on this segment of
the wire and this segment

00:04:55.840 --> 00:04:56.640
of the wire.

00:04:56.640 --> 00:04:59.080
Because they aren't in any
way perpendicular.

00:04:59.080 --> 00:05:01.800
No components of them are
even perpendicular.

00:05:01.800 --> 00:05:02.530
So fair enough.

00:05:02.530 --> 00:05:05.250
So all we know right now is the
magnetic field is exerting

00:05:05.250 --> 00:05:08.860
a downward force on this
side of our paper

00:05:08.860 --> 00:05:10.310
clip or of our circuit.

00:05:10.310 --> 00:05:11.620
Now what about this side?

00:05:11.620 --> 00:05:12.230
Well, same thing.

00:05:12.230 --> 00:05:13.940
Take the cross product.

00:05:13.940 --> 00:05:18.300
If this is our L, L cross B.

00:05:18.300 --> 00:05:22.380
So take your index finger
in the direction--.

00:05:22.380 --> 00:05:25.760
So index finger goes
like that.

00:05:25.760 --> 00:05:28.040
Your middle finger will go in
the direction of the field.

00:05:28.040 --> 00:05:31.190
So your middle finger is going
to look something like that.

00:05:31.190 --> 00:05:32.330
And then your other
two fingers are

00:05:32.330 --> 00:05:33.490
going to be like that.

00:05:33.490 --> 00:05:34.770
And what is your thumb
going to do?

00:05:34.770 --> 00:05:36.720
And this has to be your
right hand to work.

00:05:36.720 --> 00:05:38.320
Your thumb is going to
point straight up.

00:05:38.320 --> 00:05:40.000
This is like the heel
of your thumb.

00:05:40.000 --> 00:05:42.500
Your thumb is going to--.

00:05:42.500 --> 00:05:44.530
I don't know if that's a good
drawing of a thumb.

00:05:44.530 --> 00:05:48.290
But your thumb is essentially
pointing out of the page.

00:05:48.290 --> 00:05:50.710
Middle finger in the direction
of the current, or in the

00:05:50.710 --> 00:05:52.960
direction of our length.

00:05:52.960 --> 00:05:54.690
Sorry, index finger in the
direction of the current.

00:05:54.690 --> 00:05:56.460
Middle finger in the direction
of the field.

00:05:56.460 --> 00:05:58.170
Thumb points out of the page.

00:05:58.170 --> 00:06:00.270
Do that with your own right hand
and you'll see that the

00:06:00.270 --> 00:06:02.360
net force of the magnetic field
on this segment of the

00:06:02.360 --> 00:06:05.490
wire is going to be upwards.

00:06:05.490 --> 00:06:06.720
Let me do it in a different
color just to get some

00:06:06.720 --> 00:06:09.910
contrast.

00:06:09.910 --> 00:06:10.800
So what's going to happen?

00:06:10.800 --> 00:06:13.770
Assuming that this circuit
can rotate,

00:06:13.770 --> 00:06:14.880
what's going to happen?

00:06:14.880 --> 00:06:18.150
On this side there's
a downward force.

00:06:18.150 --> 00:06:20.260
On this side there's
an upward force.

00:06:20.260 --> 00:06:22.520
So the magnetic field is
actually exerting a

00:06:22.520 --> 00:06:24.380
torque on this wire.

00:06:27.100 --> 00:06:29.940
If you viewed this little dotted
line as our axis of

00:06:29.940 --> 00:06:35.190
rotation, the whole coil is
actually going to rotate

00:06:35.190 --> 00:06:36.400
around that line.

00:06:36.400 --> 00:06:39.890
And so there's some force over
here, along this whole line

00:06:39.890 --> 00:06:41.610
being applied downwards.

00:06:41.610 --> 00:06:43.230
And it's actually perpendicular

00:06:43.230 --> 00:06:45.250
to our moment arm.

00:06:45.250 --> 00:06:47.980
If you remember what we had
learned about torque.

00:06:47.980 --> 00:06:50.930
So it will actually exert all
of that force-- that force

00:06:50.930 --> 00:06:52.890
times this distance
will be the torque

00:06:52.890 --> 00:06:54.480
applied on this side.

00:06:54.480 --> 00:06:58.740
And then likewise there's a
torque-- it's really the same

00:06:58.740 --> 00:07:01.650
sign, in the same direction,
because here on the other side

00:07:01.650 --> 00:07:03.760
of the arm it's pushing
upwards.

00:07:03.760 --> 00:07:04.770
So they're not going
to cancel out.

00:07:04.770 --> 00:07:06.330
They're both going
to reinforce.

00:07:06.330 --> 00:07:08.820
And this whole coil
is going to be

00:07:08.820 --> 00:07:13.030
turning in this direction.

00:07:13.030 --> 00:07:15.690
Here it's going to be moving up
out of your video screen.

00:07:15.690 --> 00:07:18.950
Here it's going to be moving
down into your video screen.

00:07:18.950 --> 00:07:20.440
Now what happens?

00:07:20.440 --> 00:07:23.190
I'm going to try to not run
out of time either.

00:07:23.190 --> 00:07:25.100
So it's going to
start rotating.

00:07:25.100 --> 00:07:27.930
So the left hand side's going
to go below the page.

00:07:27.930 --> 00:07:29.630
The right hand side's going
to be above the page.

00:07:29.630 --> 00:07:31.015
I want to draw some perspective,
that's why I'm

00:07:31.015 --> 00:07:32.610
just drawing it bigger.

00:07:32.610 --> 00:07:35.150
Maybe it looks like that.

00:07:38.150 --> 00:07:40.950
Maybe my circuit starts
to look like that.

00:07:45.170 --> 00:07:48.926
And I'll redraw my
axis of rotation.

00:07:48.926 --> 00:07:51.250
So this is my axis
of rotation.

00:07:51.250 --> 00:07:54.220
And on the way I drew it--
this part, the axis of

00:07:54.220 --> 00:07:57.280
rotation is still in the
plane of our video.

00:07:57.280 --> 00:07:59.190
But this part of the
coil is, you could

00:07:59.190 --> 00:08:00.250
imagine it popping out.

00:08:00.250 --> 00:08:01.950
I wish you had 3D glasses on.

00:08:01.950 --> 00:08:03.630
It's popping out
of your screen.

00:08:03.630 --> 00:08:06.720
This part is going
into your screen.

00:08:06.720 --> 00:08:08.450
And the current is still going
in the same direction.

00:08:08.450 --> 00:08:11.940
Current is going in that
direction there.

00:08:11.940 --> 00:08:16.810
So using the same right hand
rule, on this side of the wire

00:08:16.810 --> 00:08:19.130
the magnetic field is going
to be exerting a

00:08:19.130 --> 00:08:21.420
net downward force.

00:08:21.420 --> 00:08:25.370
But the torque is actually going
to be less because our

00:08:25.370 --> 00:08:28.320
moment arm distance is going to
be like-- I want to draw it

00:08:28.320 --> 00:08:29.890
with some perspective.

00:08:29.890 --> 00:08:32.600
It's going to look something
like that.

00:08:32.600 --> 00:08:36.780
So it's going to be going to the
left and behind the page

00:08:36.780 --> 00:08:38.929
while the torque is still
just into the page.

00:08:38.929 --> 00:08:40.630
So you would actually take the
component of the torque that's

00:08:40.630 --> 00:08:41.809
perpendicular.

00:08:41.809 --> 00:08:43.720
So there's some component of
the torque that's actually

00:08:43.720 --> 00:08:44.169
perpendicular.

00:08:44.169 --> 00:08:45.460
I don't want to confuse
you too much.

00:08:45.460 --> 00:08:48.000
But you could imagine
the torque lessens.

00:08:48.000 --> 00:08:50.630
Even though the net magnetic
force is the same, the

00:08:50.630 --> 00:08:54.900
component of that force that's
perpendicular to your moment

00:08:54.900 --> 00:08:56.150
arm, that lessens.

00:08:56.150 --> 00:08:58.500
So there's still going to be
some torque that's going to be

00:08:58.500 --> 00:09:02.680
causing it to rotate downwards
in that direction.

00:09:02.680 --> 00:09:03.000
Sorry.

00:09:03.000 --> 00:09:03.700
You know what?

00:09:03.700 --> 00:09:05.520
I drew this wrong here.

00:09:05.520 --> 00:09:07.740
We're pushing up on the right
hand side, we're pushing down

00:09:07.740 --> 00:09:08.410
on the left hand side.

00:09:08.410 --> 00:09:14.030
So the direction is going
to be like that.

00:09:14.030 --> 00:09:16.510
Pushing up on the right hand,
down on the left hand.

00:09:16.510 --> 00:09:18.670
So you're still going to be
doing the same thing here.

00:09:18.670 --> 00:09:20.215
You are going to be
pushing up here.

00:09:20.215 --> 00:09:24.880
But you're going to be pushing
up directly out of the page.

00:09:24.880 --> 00:09:26.610
But that's not completely
perpendicular

00:09:26.610 --> 00:09:30.050
to the moment arm.

00:09:30.050 --> 00:09:33.100
So the component that is
perpendicular, that's actually

00:09:33.100 --> 00:09:35.215
creating rotational torque,
that's going

00:09:35.215 --> 00:09:36.090
to be a little less.

00:09:36.090 --> 00:09:38.370
And then you could imagine that
all the way to the point,

00:09:38.370 --> 00:09:43.470
the coil's going to keep
rotating with smaller torque.

00:09:43.470 --> 00:09:47.260
At some point you'll be
looking at it head on.

00:09:47.260 --> 00:09:50.220
So I can just draw it like
a straight line, right?

00:09:50.220 --> 00:09:51.000
You can imagine.

00:09:51.000 --> 00:09:53.710
This arm is on top and this
arm is behind it.

00:09:53.710 --> 00:09:56.260
And at this point, what's
going to happen?

00:09:56.260 --> 00:09:58.360
All the magnetic force on
this top arm is going

00:09:58.360 --> 00:10:00.740
to be popping up.

00:10:00.740 --> 00:10:02.860
It's going to be popping up out
of your page but it's not

00:10:02.860 --> 00:10:04.400
going to be providing
any torque.

00:10:04.400 --> 00:10:08.270
Because it's not perpendicular
anymore to your moment arm.

00:10:08.270 --> 00:10:11.610
And likewise, on the bottom
behind this, if you could

00:10:11.610 --> 00:10:14.760
visualize this, it would be
exerting a net downward force.

00:10:14.760 --> 00:10:16.260
And that's also not going
to be helpful.

00:10:16.260 --> 00:10:20.510
But maybe they have some angular
momentum so the wire

00:10:20.510 --> 00:10:23.130
will still rotate.

00:10:23.130 --> 00:10:24.220
But then when it still rotates,

00:10:24.220 --> 00:10:25.390
what's going to happen?

00:10:25.390 --> 00:10:26.610
And this is where I'll
leave you with a

00:10:26.610 --> 00:10:29.370
little bit of a conundrum.

00:10:29.370 --> 00:10:31.490
Actually, I don't want to go
over the Youtube limit, so I'm

00:10:31.490 --> 00:10:33.730
going to continue this in the
next video and I'll show you

00:10:33.730 --> 00:10:34.110
the conundrum.

00:10:34.110 --> 00:10:35.670
See you soon.


Magnetic force between two currents going in the same direction

WEBVTT
Kind: captions
Language: en

00:00:00.890 --> 00:00:05.660
We've now learned that a current
or a stream of moving

00:00:05.660 --> 00:00:08.330
charges can be affected
by a magnetic field.

00:00:08.330 --> 00:00:12.280
And we've also learned that it
can induce a magnetic field.

00:00:12.280 --> 00:00:16.430
So that begs the question,
what is the effect of one

00:00:16.430 --> 00:00:19.980
current carrying wire on another
current carrying wire?

00:00:19.980 --> 00:00:20.760
Let's do that.

00:00:20.760 --> 00:00:26.500
Let's draw my first current
carrying wire in green.

00:00:26.500 --> 00:00:30.600
That's the first current
carrying wire.

00:00:30.600 --> 00:00:35.030
And let's say that the current
is-- it's in magenta-- and

00:00:35.030 --> 00:00:38.370
we'll call this current 1.

00:00:38.370 --> 00:00:40.270
And then I have another
current carrying

00:00:40.270 --> 00:00:41.605
wire not too far away.

00:00:49.220 --> 00:00:57.870
And I will call that
current I2.

00:00:57.870 --> 00:00:59.160
Now what else do we need
to figure out?

00:00:59.160 --> 00:01:00.230
Oh, well, let me
just tell you.

00:01:00.230 --> 00:01:03.240
Let's say that they are
a radius of r apart.

00:01:03.240 --> 00:01:06.060
And I say radius because we
learned in the last video that

00:01:06.060 --> 00:01:09.270
the magnetic field created by
a current carrying wire is

00:01:09.270 --> 00:01:11.430
kind of a, you know, they're
kind of these circular

00:01:11.430 --> 00:01:12.780
cylinders around the wire.

00:01:12.780 --> 00:01:19.410
So let's say the distance from
this wire to that wire is r.

00:01:19.410 --> 00:01:23.220
That distance is r.

00:01:23.220 --> 00:01:26.760
And so my question to you is--
well, first, just before we

00:01:26.760 --> 00:01:30.670
break into the math-- what's
going to happen?

00:01:30.670 --> 00:01:32.480
Well, we don't know the
magnitudes of the currents or

00:01:32.480 --> 00:01:33.580
anything just yet.

00:01:33.580 --> 00:01:34.520
But what's going to happen?

00:01:34.520 --> 00:01:37.690
What will be the net effect
on, let's say, this wire?

00:01:37.690 --> 00:01:40.836
Let's say for some reason this
wire is fixed or we could say

00:01:40.836 --> 00:01:42.410
they're floating in space.

00:01:42.410 --> 00:01:44.780
Let's just focus on
wire 2 for now.

00:01:44.780 --> 00:01:48.070
This is wire 2, this
is wire 1.

00:01:48.070 --> 00:01:50.460
What's going to happen
to wire 2?

00:01:50.460 --> 00:01:51.530
Well, let's think about it.

00:01:51.530 --> 00:01:53.630
Wire 1-- the current
in it is going to

00:01:53.630 --> 00:01:55.190
generate a magnetic field.

00:01:55.190 --> 00:01:57.060
Now what's the shape of
that magnetic field

00:01:57.060 --> 00:01:58.390
going to look like?

00:01:58.390 --> 00:02:02.450
Well, we could take our right
hand, do that right hand wrap

00:02:02.450 --> 00:02:03.060
around rule.

00:02:03.060 --> 00:02:04.870
It's a little different than
the cross product rule,

00:02:04.870 --> 00:02:06.520
although it's kind
of a byproduct.

00:02:06.520 --> 00:02:13.800
So that's my right hand and
I'm wrapping it around.

00:02:13.800 --> 00:02:17.380
So if I point my thumb in the
direction of the current-- so

00:02:17.380 --> 00:02:19.480
that's the direction of the
current, just like I did--

00:02:19.480 --> 00:02:21.430
then the magnetic field
goes in the

00:02:21.430 --> 00:02:23.360
direction of my fingers.

00:02:23.360 --> 00:02:28.900
So they're going to go
around this wire.

00:02:28.900 --> 00:02:32.323
And so if I were to just draw
the magnetic field where it

00:02:32.323 --> 00:02:36.010
intersects with this screen, on
the right hand side it will

00:02:36.010 --> 00:02:37.120
go into the screen.

00:02:37.120 --> 00:02:39.700
So we'll just see the
rear ends of the

00:02:39.700 --> 00:02:41.560
magnetic field line.

00:02:41.560 --> 00:02:43.190
And I'll draw it in the same
color as the current, so you

00:02:43.190 --> 00:02:44.580
know it's being created by I1.

00:02:47.650 --> 00:02:53.700
So I1-- its effect keeps going
out to infinity, although it

00:02:53.700 --> 00:02:55.770
gets much weaker
as we learned.

00:02:55.770 --> 00:02:58.480
It's inversely proportional
with r.

00:02:58.480 --> 00:02:59.720
But this is the field of I1.

00:02:59.720 --> 00:03:01.580
I can draw these-- I
don't want to crowd

00:03:01.580 --> 00:03:03.200
my page up too much.

00:03:03.200 --> 00:03:05.110
And then on this side
of I1, what happens?

00:03:05.110 --> 00:03:06.710
Well, on this side,
you can see the

00:03:06.710 --> 00:03:07.980
fingers come back around.

00:03:07.980 --> 00:03:09.860
So it pops out when
it intersects

00:03:09.860 --> 00:03:12.660
with your video monitor.

00:03:12.660 --> 00:03:16.720
So on this side, the vectors--
this is the top of an arrow,

00:03:16.720 --> 00:03:19.960
coming out at you.

00:03:19.960 --> 00:03:21.050
Fair enough.

00:03:21.050 --> 00:03:24.410
So I1, by going in this
direction, is generating a

00:03:24.410 --> 00:03:27.870
magnetic field that, at least
where I2 is concerned, that

00:03:27.870 --> 00:03:33.590
magnetic field is going
into the page.

00:03:33.590 --> 00:03:36.070
So what was our formula?

00:03:36.070 --> 00:03:38.530
And this all came from the
first formula we learned

00:03:38.530 --> 00:03:39.960
about, the effect of a magnetic
field soon. on a

00:03:39.960 --> 00:03:40.510
moving charge.

00:03:40.510 --> 00:03:44.470
But what was the formula of the
net magnetic force on a

00:03:44.470 --> 00:03:46.500
current carrying wire?

00:03:46.500 --> 00:03:56.050
It was the force-- I'll do it in
blue-- it's a vector, has a

00:03:56.050 --> 00:03:59.420
magnitude and direction--
is equal to the current.

00:03:59.420 --> 00:04:02.820
Well, in this case, we want
to know the force on this

00:04:02.820 --> 00:04:04.940
current, on current 2, right?

00:04:04.940 --> 00:04:09.160
Caused by this magnetic field,
by magnetic field 1.

00:04:09.160 --> 00:04:16.220
So it will be equal to I2, the
magnitude of this current,

00:04:16.220 --> 00:04:20.250
times L-- where L is-- because
you can't just say, oh well,

00:04:20.250 --> 00:04:21.370
what is the effect
on this wire?

00:04:21.370 --> 00:04:24.160
You have to know how much wire
is under consideration.

00:04:24.160 --> 00:04:26.520
So let's say we have
a length of wire.

00:04:26.520 --> 00:04:28.240
And then of course, if you know
the length of wire and we

00:04:28.240 --> 00:04:30.110
knew its mass and we knew the
force on it, we could figure

00:04:30.110 --> 00:04:31.570
out its acceleration
in some directions.

00:04:31.570 --> 00:04:34.120
So let's say that
this distance is

00:04:34.120 --> 00:04:35.800
L, and it's a vector.

00:04:35.800 --> 00:04:38.540
L goes in the same direction
as the current.

00:04:38.540 --> 00:04:39.790
That's just the convention
we're using.

00:04:39.790 --> 00:04:41.420
It makes things simple.

00:04:41.420 --> 00:04:44.010
So that's L.

00:04:44.010 --> 00:04:50.680
So the force on this wire, or at
least the length L of this

00:04:50.680 --> 00:04:55.720
wire, is going to be equal
to current 2 times L.

00:04:55.720 --> 00:04:58.840
We could call that even L2, just
so that you know that it

00:04:58.840 --> 00:04:59.980
deals with wire 2.

00:04:59.980 --> 00:05:02.400
That's a vector quantity.

00:05:02.400 --> 00:05:03.420
I could make it a full arrow.

00:05:03.420 --> 00:05:03.940
Doesn't matter.

00:05:03.940 --> 00:05:04.670
It's just a notation.

00:05:04.670 --> 00:05:06.870
I've seen professors do it
either way, I've seen it

00:05:06.870 --> 00:05:08.780
written either way, as well.

00:05:08.780 --> 00:05:12.180
Cross the magnetic field
that it's in.

00:05:12.180 --> 00:05:14.150
What's the magnetic field
that it's in?

00:05:14.150 --> 00:05:16.080
The magnetic field-- I'll do
it in magenta, because it's

00:05:16.080 --> 00:05:18.770
the magnetic field created
by current 1.

00:05:18.770 --> 00:05:26.670
So it's magnetic field 1, which
is this magnetic field.

00:05:26.670 --> 00:05:30.960
So before going into the math,
let's just figure out what

00:05:30.960 --> 00:05:33.380
direction is this net force
going to be in?

00:05:33.380 --> 00:05:37.000
So here we say, well, the
current is a scalar, so that's

00:05:37.000 --> 00:05:38.470
not going to affect
the direction.

00:05:38.470 --> 00:05:40.850
What's the direction of L2?

00:05:40.850 --> 00:05:42.290
This is L2.

00:05:42.290 --> 00:05:44.640
I didn't label it L2
on the diagram.

00:05:44.640 --> 00:05:46.190
What's the direction of L2?

00:05:46.190 --> 00:05:47.180
Well, it's up.

00:05:47.180 --> 00:05:50.650
And then the direction of B1,
the magnetic field created by

00:05:50.650 --> 00:05:53.400
current 1, is going into
the page here.

00:05:53.400 --> 00:05:57.520
So here we just do the standard
cross product.

00:05:57.520 --> 00:05:59.380
Let me see if I can
pull this off.

00:05:59.380 --> 00:06:01.400
This is actually an
easy one to draw.

00:06:01.400 --> 00:06:08.660
So I put my index finger
in the direction of L2.

00:06:08.660 --> 00:06:10.560
And then I put my middle
finger in the

00:06:10.560 --> 00:06:11.760
direction of the field.

00:06:11.760 --> 00:06:13.500
So my middle finger's going
to point straight

00:06:13.500 --> 00:06:15.560
down into this page.

00:06:15.560 --> 00:06:17.880
My other fingers just do what
they would naturally do.

00:06:17.880 --> 00:06:19.290
And then my thumb
would go in the

00:06:19.290 --> 00:06:20.220
direction of the net force.

00:06:20.220 --> 00:06:23.190
This is just the
cross product.

00:06:23.190 --> 00:06:25.700
You'll see teachers teach the
cross product other ways,

00:06:25.700 --> 00:06:27.720
where they tell you to put your
thumb in the direction of

00:06:27.720 --> 00:06:29.780
the field, and this and
that, your palm--

00:06:29.780 --> 00:06:30.590
those are all valid.

00:06:30.590 --> 00:06:32.030
They're just different
variations of the same thing.

00:06:32.030 --> 00:06:33.580
I find this one easier
to remember.

00:06:33.580 --> 00:06:35.910
Because when I take the cross
product, index finger is the

00:06:35.910 --> 00:06:36.900
first term of the
cross product.

00:06:36.900 --> 00:06:39.040
Middle finger is the second
term of the cross product.

00:06:39.040 --> 00:06:42.980
Thumb is the direction
of the cross product.

00:06:42.980 --> 00:06:46.830
So anyway, this is the
direction of L2.

00:06:46.830 --> 00:06:49.300
The magnetic field, we already
know, goes into the page.

00:06:49.300 --> 00:06:53.350
So my middle finger is
going into the page.

00:06:53.350 --> 00:06:56.510
And my thumb is in the direction
of the force on the

00:06:56.510 --> 00:06:57.620
magnetic field.

00:06:57.620 --> 00:07:00.560
So that's the direction
of the force.

00:07:00.560 --> 00:07:02.180
So there you have it.

00:07:02.180 --> 00:07:05.420
If this current is moving in
this direction and its field

00:07:05.420 --> 00:07:08.580
is-- we know from this wrap
around rule that pops out here

00:07:08.580 --> 00:07:10.950
and it goes in here-- the effect
that it has on this

00:07:10.950 --> 00:07:15.260
other wire is that where the
current is going in the same

00:07:15.260 --> 00:07:17.430
direction, is that it
will be attracted.

00:07:17.430 --> 00:07:22.130
So the net force you is going
in that direction.

00:07:22.130 --> 00:07:26.870
We could say the force
from 1 on 2.

00:07:26.870 --> 00:07:27.900
That's just my convention.

00:07:27.900 --> 00:07:30.300
Maybe other people would have
written it the force

00:07:30.300 --> 00:07:33.780
given to 2 by 1.

00:07:33.780 --> 00:07:36.170
That's the force given
by 1 to 2.

00:07:36.170 --> 00:07:37.750
That's how I'm writing it.

00:07:37.750 --> 00:07:42.540
Now what's going to be the force
on current 1 from I2?

00:07:42.540 --> 00:07:44.040
Well, it's going to be the
current-- well, it's going to

00:07:44.040 --> 00:07:45.350
be the force there.

00:07:45.350 --> 00:07:47.460
Well it's going to be
the same thing.

00:07:47.460 --> 00:07:50.190
Let me draw I2's
magnetic field.

00:07:50.190 --> 00:07:52.600
You do the wrap around rule,
it's going to look the same.

00:07:52.600 --> 00:07:56.200
So I2, sure, on this side its
field is going to be going

00:07:56.200 --> 00:07:59.240
into the page.

00:07:59.240 --> 00:08:01.280
But what's I2's field going
to be doing here?

00:08:01.280 --> 00:08:02.600
It's going to be popping out.

00:08:05.960 --> 00:08:07.800
I just did the wrap around--
take this wrap around, wrap it

00:08:07.800 --> 00:08:09.280
around that wire.

00:08:09.280 --> 00:08:11.880
So that's the field of I2.

00:08:11.880 --> 00:08:19.250
So then we can write down that
the force-- and let's take, I

00:08:19.250 --> 00:08:22.660
don't know, this is
some distance.

00:08:22.660 --> 00:08:25.300
Let's call that L1.

00:08:25.300 --> 00:08:33.860
So the force from current 2 on
wire 1 of length L1, from here

00:08:33.860 --> 00:08:44.940
to here, is equal to current 1
times L1-- which is a vector--

00:08:44.940 --> 00:08:48.950
cross the magnetic field
created by current 2.

00:08:53.430 --> 00:08:55.460
And so we can do the same
cross product here.

00:08:55.460 --> 00:09:01.510
Put our index finger in
the direction of L1.

00:09:01.510 --> 00:09:02.930
That's what you do with
the first element

00:09:02.930 --> 00:09:04.140
of the cross product.

00:09:04.140 --> 00:09:07.820
And then you put your middle
finger in the direction of B2.

00:09:07.820 --> 00:09:10.800
And then your thumb is going to
tell you what the net force

00:09:10.800 --> 00:09:11.260
is going to be.

00:09:11.260 --> 00:09:12.810
So let me draw that.

00:09:12.810 --> 00:09:16.360
So let me draw my hand.

00:09:16.360 --> 00:09:18.390
And just so you know, before I
do any of these, I actually

00:09:18.390 --> 00:09:20.800
look at my hand, just
to make sure I'm

00:09:20.800 --> 00:09:21.450
drawing the right thing.

00:09:21.450 --> 00:09:26.020
So my index finger in the
direction of I1, my middle

00:09:26.020 --> 00:09:28.710
finger-- sorry, my index finger
in the direction of L1,

00:09:28.710 --> 00:09:31.750
which is the same as I1, and
then my middle finger is going

00:09:31.750 --> 00:09:33.160
to do what the magnetic
field is doing.

00:09:33.160 --> 00:09:34.560
So my middle finger is actually
going to point

00:09:34.560 --> 00:09:36.300
straight up.

00:09:36.300 --> 00:09:39.220
And then my other fingers are
just going to do what they do.

00:09:39.220 --> 00:09:41.790
And so now you're looking
at the palm of my hand.

00:09:41.790 --> 00:09:47.350
And my thumb-- let me make sure
I'm doing this correctly.

00:09:47.350 --> 00:09:48.600
Oh, no.

00:09:50.990 --> 00:09:53.370
I was drawing my left hand.

00:09:53.370 --> 00:09:54.850
See, that's an error.

00:09:54.850 --> 00:09:56.400
You don't want to draw your left
hand when you're doing

00:09:56.400 --> 00:09:58.280
the right hand rule with
cross products.

00:09:58.280 --> 00:10:01.630
So let me draw it down here.

00:10:01.630 --> 00:10:04.470
My index finger going in
the direction of L1.

00:10:07.280 --> 00:10:11.180
My middle finger's popping
straight up, because the

00:10:11.180 --> 00:10:14.040
magnetic field created by
I2 is popping straight

00:10:14.040 --> 00:10:15.080
out of the page here.

00:10:15.080 --> 00:10:17.460
So my middle finger goes
straight up and my other

00:10:17.460 --> 00:10:19.830
fingers do what they
need to do.

00:10:19.830 --> 00:10:21.860
Looking at the palm.

00:10:21.860 --> 00:10:24.460
And then my thumb will
go in that direction.

00:10:24.460 --> 00:10:30.290
So the cross product of L with
B2 popping out of this page,

00:10:30.290 --> 00:10:33.050
the net force is going to
be in this direction.

00:10:33.050 --> 00:10:35.110
So there's a little bit
of symmetry here.

00:10:35.110 --> 00:10:37.920
This wire's going to be
attracted towards that wire,

00:10:37.920 --> 00:10:40.420
and this wire's going to be
attracted to that wire.

00:10:40.420 --> 00:10:42.240
They're both going to--
eventually if they were

00:10:42.240 --> 00:10:45.220
floating in space, they would
slowly get closer and closer

00:10:45.220 --> 00:10:47.000
to each other and their radiuses
would get closer and

00:10:47.000 --> 00:10:50.370
closer and they would accelerate
to each other, at

00:10:50.370 --> 00:10:52.310
ever increasing rates
actually.

00:10:52.310 --> 00:10:53.540
Anyway, I'm out of time.

00:10:53.540 --> 00:10:56.480
In the next video I'll do this
same principle, but we'll do

00:10:56.480 --> 00:10:57.380
it with some numbers.

00:10:57.380 --> 00:10:58.630
See


Magnetic field created by a current carrying wire

WEBVTT
Kind: captions
Language: en

00:00:00.900 --> 00:00:06.040
So not only can a magnetic field
exert some force on a

00:00:06.040 --> 00:00:09.230
moving charge, we're now going
to learn that a moving charge

00:00:09.230 --> 00:00:12.160
or a current can actually
create a magnetic field.

00:00:12.160 --> 00:00:15.010
So there is some type
of symmetry here.

00:00:15.010 --> 00:00:18.600
And as we'll learn later when
we learn our calculus and we

00:00:18.600 --> 00:00:25.810
do this in a slightly more
rigorous way, we'll see that

00:00:25.810 --> 00:00:29.010
magnetic fields and electric
fields are actually two sides

00:00:29.010 --> 00:00:32.430
of the same coin, of
electromagnetic fields.

00:00:32.430 --> 00:00:33.880
But anyway, we won't worry
about that now.

00:00:33.880 --> 00:00:36.260
And I think it's enough to
ponder right now that a

00:00:36.260 --> 00:00:39.220
current can actually induce
a magnetic field.

00:00:39.220 --> 00:00:40.570
And actually, just
a moving electron

00:00:40.570 --> 00:00:42.320
creates a magnetic field.

00:00:42.320 --> 00:00:45.110
And it does it in a surface of a
sphere-- I won't go into all

00:00:45.110 --> 00:00:45.500
that right now.

00:00:45.500 --> 00:00:47.500
Because the math gets a little
bit fancy there.

00:00:47.500 --> 00:00:50.600
But what you might encounter in
your standard high school

00:00:50.600 --> 00:00:52.950
physics class-- that's not
getting deeply into vector

00:00:52.950 --> 00:00:57.180
calculus-- is that if you
just have a wire--

00:00:57.180 --> 00:00:58.820
let me draw a wire.

00:00:58.820 --> 00:01:00.780
That's my wire.

00:01:00.780 --> 00:01:10.030
And it's carrying some current
I, it turns out that this wire

00:01:10.030 --> 00:01:12.230
will generate a magnetic
field.

00:01:12.230 --> 00:01:14.840
And the shape of that magnetic
field is going to be

00:01:14.840 --> 00:01:19.960
co-centric circles
around this wire.

00:01:19.960 --> 00:01:22.730
Let me see if I can draw that.

00:01:22.730 --> 00:01:25.730
So here I'll draw it just like
how I do when I try to do

00:01:25.730 --> 00:01:29.510
rotations of solids in
the calculus video.

00:01:29.510 --> 00:01:34.120
So the magnetic field would go
behind and in front and it

00:01:34.120 --> 00:01:37.730
goes like that.

00:01:37.730 --> 00:01:40.130
Or another way you can think
about it is if-- let's go down

00:01:40.130 --> 00:01:42.930
here-- is on the left
side of this wire.

00:01:42.930 --> 00:01:45.840
If you say that the wire's in
the plane of this video, the

00:01:45.840 --> 00:01:49.110
magnetic field is popping
out of your screen.

00:01:52.650 --> 00:01:55.500
And on this side, on the right
side, the magnetic field is

00:01:55.500 --> 00:01:57.980
popping into the screen.

00:01:57.980 --> 00:02:00.000
It's going into the screen.

00:02:00.000 --> 00:02:01.400
And you could imagine
that, right?

00:02:01.400 --> 00:02:04.840
You could imagine if, on this
drawing up here, you could say

00:02:04.840 --> 00:02:06.370
this is where it intersects
the screen.

00:02:06.370 --> 00:02:09.240
All of this is kind of
behind the screen.

00:02:09.240 --> 00:02:11.440
And all of this is in
front of the screen.

00:02:11.440 --> 00:02:13.460
And this is where it's
popping out.

00:02:13.460 --> 00:02:15.430
And this is where it's popping
into the screen.

00:02:15.430 --> 00:02:16.770
Hopefully that makes a
little bit of sense.

00:02:16.770 --> 00:02:20.180
And how did I know that it's
rotating this way?

00:02:20.180 --> 00:02:22.370
Well, it actually does come out
of the cross product when

00:02:22.370 --> 00:02:24.950
you do it with a regular
charge and all of that.

00:02:24.950 --> 00:02:26.740
But we're not going to go
into that right now.

00:02:26.740 --> 00:02:28.670
And so there's a different
right hand rule

00:02:28.670 --> 00:02:29.640
that you can use.

00:02:29.640 --> 00:02:34.130
And it's literally you hold
this wire, or you imagine

00:02:34.130 --> 00:02:37.810
holding this wire, with your
right hand with your thumb

00:02:37.810 --> 00:02:39.570
going in the direction
of the current.

00:02:39.570 --> 00:02:42.010
And if you hold this wire with
your thumb going in the

00:02:42.010 --> 00:02:44.790
direction of the current, your
fingers are going to go in the

00:02:44.790 --> 00:02:47.890
direction of the
magnetic field.

00:02:47.890 --> 00:02:51.030
So let me see if I
can draw that.

00:02:51.030 --> 00:02:52.830
I will draw it in blue.

00:02:52.830 --> 00:02:58.070
So if this is my thumb, my thumb
is going along the top

00:02:58.070 --> 00:03:00.690
of the wire.

00:03:00.690 --> 00:03:03.045
And then my hand is curling
around the wire.

00:03:06.000 --> 00:03:06.700
Those are my knuckles.

00:03:06.700 --> 00:03:09.380
Those are the veins
on my hand.

00:03:09.380 --> 00:03:12.210
This is my nail.

00:03:12.210 --> 00:03:16.490
So as you can see, if I was
holding that same wire-- let

00:03:16.490 --> 00:03:17.760
me draw the wire.

00:03:17.760 --> 00:03:21.490
So if I was holding that same
wire, we see that my thumb is

00:03:21.490 --> 00:03:22.970
going in the direction
of the current.

00:03:22.970 --> 00:03:25.910
So this is a slightly new
thing to memorize.

00:03:25.910 --> 00:03:27.730
And what is the magnetic
field doing?

00:03:27.730 --> 00:03:30.840
Well, it's going in the
direction of my fingers.

00:03:30.840 --> 00:03:33.930
My fingers are popping out
on this side of the wire.

00:03:33.930 --> 00:03:35.760
They're coming out on this
side of the wire.

00:03:35.760 --> 00:03:37.560
And they're going in, or
at least my hand is

00:03:37.560 --> 00:03:39.460
going in, on that side.

00:03:39.460 --> 00:03:42.490
It's going into the screen.

00:03:42.490 --> 00:03:44.570
Hopefully that makes sense.

00:03:44.570 --> 00:03:46.070
Now, how can we quantify?

00:03:46.070 --> 00:03:48.280
Well, before we quantify, let's
get a little bit more of

00:03:48.280 --> 00:03:49.890
the intuition of what's
happening.

00:03:49.890 --> 00:03:52.730
It turns out that the closer
you get to the wire, the

00:03:52.730 --> 00:03:56.290
stronger the magnetic field, and
the further you get out,

00:03:56.290 --> 00:03:57.800
the weaker the magnetic field.

00:03:57.800 --> 00:04:00.510
And that kind of makes sense
if you imagine the magnetic

00:04:00.510 --> 00:04:01.760
field spreading out.

00:04:04.380 --> 00:04:06.460
I don't want to go into too
sophisticated analogies.

00:04:06.460 --> 00:04:08.830
But if you imagine the magnetic
field spreading out,

00:04:08.830 --> 00:04:10.580
and as it goes further and
further out it kind of gets

00:04:10.580 --> 00:04:12.705
distributed over a wider and
wider circumference.

00:04:12.705 --> 00:04:15.270
And actually the formula I'm
going to give you kind of has

00:04:15.270 --> 00:04:16.870
a taste for that.

00:04:16.870 --> 00:04:20.450
So the formula for the magnetic
field-- and it really

00:04:20.450 --> 00:04:23.110
is defined with a cross product
and things like that,

00:04:23.110 --> 00:04:25.920
but for our purposes we won't
worry about that.

00:04:25.920 --> 00:04:29.350
You'll just have to know that
this is the shape if the

00:04:29.350 --> 00:04:30.950
current is going in
that direction.

00:04:30.950 --> 00:04:33.880
And, of course, if the current
was going downwards then the

00:04:33.880 --> 00:04:35.550
magnetic field would just
reverse directions.

00:04:35.550 --> 00:04:36.640
But it would still
be in co-centric

00:04:36.640 --> 00:04:38.220
circles around the wire.

00:04:38.220 --> 00:04:42.870
But anyway, what is the
magnitude of that field?

00:04:42.870 --> 00:04:49.630
The magnitude of that magnetic
field is equal to mu-- which

00:04:49.630 --> 00:04:52.240
is a Greek letter, which I will
explain in a second--

00:04:52.240 --> 00:04:58.120
times the current divided
by 2 pi r.

00:04:58.120 --> 00:05:00.590
So this has a little bit
of a feel for what

00:05:00.590 --> 00:05:01.280
I was saying before.

00:05:01.280 --> 00:05:04.430
That the further you go out--
where r is how far you are

00:05:04.430 --> 00:05:09.410
from the wire-- the further you
go out, if r gets bigger,

00:05:09.410 --> 00:05:12.750
the magnitude of the magnetic
field is going to get weaker.

00:05:12.750 --> 00:05:14.650
And this 2 pi r, that
looks a lot like the

00:05:14.650 --> 00:05:16.140
circumference of a circle.

00:05:16.140 --> 00:05:17.225
So that gives you
a taste for it.

00:05:17.225 --> 00:05:20.730
I know I haven't proved
anything rigorously.

00:05:20.730 --> 00:05:22.730
But it at least gives you a
sense of, look there's a

00:05:22.730 --> 00:05:23.450
little formula for

00:05:23.450 --> 00:05:24.350
circumference of a circle here.

00:05:24.350 --> 00:05:25.400
And that kind of makes
sense, right?

00:05:25.400 --> 00:05:27.280
Because the magnetic
field at that point

00:05:27.280 --> 00:05:29.770
is kind of a circle.

00:05:29.770 --> 00:05:33.940
The magnitude is equal at an
equal radius around that wire.

00:05:33.940 --> 00:05:36.770
Now what is this mu, this thing
that looks like a u?

00:05:36.770 --> 00:05:39.380
Well, that's the permeability
of the material

00:05:39.380 --> 00:05:40.330
that the wire's in.

00:05:40.330 --> 00:05:41.990
So the magnetic field is
actually going to have a

00:05:41.990 --> 00:05:44.820
different strength depending on
whether this wire is going

00:05:44.820 --> 00:05:48.420
through rubber, whether it's
going through a vacuum, or

00:05:48.420 --> 00:05:50.840
air, or metal, or water.

00:05:50.840 --> 00:05:54.400
And for the purposes of your
high school physics class, we

00:05:54.400 --> 00:05:56.990
assume that it's going
through air normally.

00:05:56.990 --> 00:06:01.930
And the value for air
is pretty close to

00:06:01.930 --> 00:06:03.310
the value for a vacuum.

00:06:03.310 --> 00:06:05.600
And it's called the permeability
of a vacuum.

00:06:05.600 --> 00:06:07.410
And I forget what
that value is.

00:06:07.410 --> 00:06:08.200
I could look it up.

00:06:08.200 --> 00:06:09.820
But it actually turns
out that your

00:06:09.820 --> 00:06:11.010
calculator has that value.

00:06:11.010 --> 00:06:12.710
So let's do a problem,
just to put some

00:06:12.710 --> 00:06:14.580
numbers to the formula.

00:06:14.580 --> 00:06:19.460
So let's say I had this current
and it is-- I don't

00:06:19.460 --> 00:06:22.032
know, the current is equal
to-- I'm going

00:06:22.032 --> 00:06:22.780
to make up a number.

00:06:22.780 --> 00:06:25.740
2 amperes.

00:06:25.740 --> 00:06:33.320
And let's say that I just pick
a point right here that is--

00:06:33.320 --> 00:06:36.670
let's say that that's
3 meters away

00:06:36.670 --> 00:06:37.950
from the wire in question.

00:06:37.950 --> 00:06:39.980
So my question to you is what
is the magnitude in the

00:06:39.980 --> 00:06:43.760
direction of the magnetic
field right there?

00:06:43.760 --> 00:06:45.140
Well, the magnitude is easy.

00:06:45.140 --> 00:06:46.650
We just substitute
in this equation.

00:06:46.650 --> 00:06:50.540
So the magnitude of the magnetic
field at this point

00:06:50.540 --> 00:06:53.410
is equal to-- and we assume that
the wire's going through

00:06:53.410 --> 00:06:57.270
air or a vacuum-- the
permeability of free space--

00:06:57.270 --> 00:06:59.770
that's just a constant, though
it looks fancy-- times the

00:06:59.770 --> 00:07:04.910
current times 2 amperes
divided by 2 pi r.

00:07:04.910 --> 00:07:05.345
What's r?

00:07:05.345 --> 00:07:07.350
It's 3 meters.

00:07:07.350 --> 00:07:09.020
So 2 pi times 3.

00:07:09.020 --> 00:07:13.260
So it equals the permeability
of free space.

00:07:13.260 --> 00:07:13.510
So let's see.

00:07:13.510 --> 00:07:16.630
The 2 and the 2 cancel
out over 3 pi.

00:07:16.630 --> 00:07:18.350
So how do we calculate that?

00:07:18.350 --> 00:07:24.040
Well, we get out our trusty
TI-85 calculator.

00:07:24.040 --> 00:07:28.510
And I think you'll be maybe
pleasantly surprised or

00:07:28.510 --> 00:07:31.330
shocked to realize that-- I
deleted everything just so you

00:07:31.330 --> 00:07:34.280
can see how I get there--
that it actually has the

00:07:34.280 --> 00:07:36.640
permeability of free
space stored in it.

00:07:36.640 --> 00:07:39.220
So what you do is you go to
second and you press constant,

00:07:39.220 --> 00:07:41.330
which is the 4 button.

00:07:41.330 --> 00:07:43.560
It's in the built-in
constants.

00:07:43.560 --> 00:07:44.790
Let's see, it's not
one of those.

00:07:44.790 --> 00:07:46.430
You press more.

00:07:46.430 --> 00:07:48.040
It's not one of those,
press more.

00:07:48.040 --> 00:07:49.170
Oh look at that.

00:07:49.170 --> 00:07:50.700
Mu not.

00:07:50.700 --> 00:07:52.270
The permeability
of free space.

00:07:52.270 --> 00:07:54.120
That's what I need.

00:07:54.120 --> 00:07:57.190
And I have to divide
it by 3 pi.

00:07:57.190 --> 00:08:00.570
Divide it by 3-- and
then where is pi?

00:08:00.570 --> 00:08:01.210
There it is.

00:08:01.210 --> 00:08:03.000
It's over the power sign.

00:08:03.000 --> 00:08:05.880
Divided by 3 pi.

00:08:05.880 --> 00:08:10.480
It equals 1.3 times 10 to
the negative seventh.

00:08:10.480 --> 00:08:11.940
It's going to be teslas.

00:08:11.940 --> 00:08:17.820
The magnetic field is going to
be equal to 1.3 times 10 to

00:08:17.820 --> 00:08:20.270
the minus seventh teslas.

00:08:20.270 --> 00:08:23.290
So it's a fairly weak
magnetic field.

00:08:23.290 --> 00:08:27.220
And that's why you don't have
metal objects being thrown

00:08:27.220 --> 00:08:31.520
around by the wires behind
your television set.

00:08:31.520 --> 00:08:33.650
But anyway, hopefully that gives
you a little bit-- and

00:08:33.650 --> 00:08:36.289
just so you know how it
all fits together.

00:08:36.289 --> 00:08:40.700
We're saying that these moving
charges, not only can they be

00:08:40.700 --> 00:08:42.909
affected by a magnetic field,
not only can a current be

00:08:42.909 --> 00:08:45.870
affected by a magnetic field
or just a moving charge, it

00:08:45.870 --> 00:08:47.270
actually creates them.

00:08:47.270 --> 00:08:49.840
And that kind of creates a
little bit of symmetry in your

00:08:49.840 --> 00:08:50.270
head, hopefully.

00:08:50.270 --> 00:08:52.770
Because that was also true
of electric field.

00:08:52.770 --> 00:08:57.170
A charge, a stationary charge,
is obviously pulled or pushed

00:08:57.170 --> 00:08:58.760
by a static electric field.

00:08:58.760 --> 00:09:01.910
And it also creates its own
static electric field.

00:09:01.910 --> 00:09:03.640
So it's always in the
back of your mind.

00:09:03.640 --> 00:09:05.180
Because if you keep studying
physics, you're going to

00:09:05.180 --> 00:09:09.000
actually prove to yourself that
electric and magnetic

00:09:09.000 --> 00:09:11.790
fields are two sides
of the same coin.

00:09:11.790 --> 00:09:14.150
And it just looks like a
magnetic field when you're in

00:09:14.150 --> 00:09:15.930
a different frame of reference,
When something is

00:09:15.930 --> 00:09:17.020
whizzing past you.

00:09:17.020 --> 00:09:19.650
While if you were whizzing along
with it, then that thing

00:09:19.650 --> 00:09:20.350
would look static.

00:09:20.350 --> 00:09:21.830
And then it might look a
little bit more like an

00:09:21.830 --> 00:09:22.820
electric field.

00:09:22.820 --> 00:09:25.230
But anyway, I'll leave
you there now.

00:09:25.230 --> 00:09:29.160
And in the next video I will
show you what happens when we

00:09:29.160 --> 00:09:33.440
have two wires carrying current

00:09:33.440 --> 00:09:34.660
parallel to each other.

00:09:34.660 --> 00:09:37.630
And you might guess that they
might actually attract or

00:09:37.630 --> 00:09:38.560
repel each other.

00:09:38.560 --> 00:09:41.450
Anyway, I'll see you
in the next video.


Magnetic force on a current carrying wire

WEBVTT
Kind: captions
Language: en

00:00:00.790 --> 00:00:04.540
Let's explore the repercussions
of this

00:00:04.540 --> 00:00:05.590
equation some more.

00:00:05.590 --> 00:00:06.810
So what was the equation?

00:00:06.810 --> 00:00:10.300
It was that the force of a
magnetic field on a moving

00:00:10.300 --> 00:00:14.220
charged particle is equal to the
charge-- that's not what I

00:00:14.220 --> 00:00:17.860
wanted to do-- is equal to the
charge of the particle-- and

00:00:17.860 --> 00:00:21.200
that's just a scalar quantity--
times the

00:00:21.200 --> 00:00:25.520
velocity-- the cross product
of the velocity of the

00:00:25.520 --> 00:00:30.620
particle-- with the
magnetic field.

00:00:30.620 --> 00:00:35.550
Now, isn't the velocity vector
just the same thing as the

00:00:35.550 --> 00:00:38.000
distance vector divided
by time?

00:00:38.000 --> 00:00:41.370
So the velocity vector is equal
to-- let's call the

00:00:41.370 --> 00:00:45.280
distance that the electron
travels, l.

00:00:45.280 --> 00:00:47.620
Distance divided by time.

00:00:47.620 --> 00:00:51.180
So we could rewrite that, that
the force vector is equal to

00:00:51.180 --> 00:00:55.780
the charge times-- and I'm doing
this on purpose-- 1 over

00:00:55.780 --> 00:00:57.600
time, right?

00:00:57.600 --> 00:01:03.720
Times the distance vector
taken-- you take the cross

00:01:03.720 --> 00:01:06.530
product with the
magnetic field.

00:01:06.530 --> 00:01:10.730
All I did is I rewrote velocity
as per time times

00:01:10.730 --> 00:01:13.140
distance, or distance
per time.

00:01:13.140 --> 00:01:15.950
And this is a scalar quantity,
at least for our purposes,

00:01:15.950 --> 00:01:17.890
time only has a magnitude.

00:01:17.890 --> 00:01:19.660
Maybe we could call
it change in time.

00:01:19.660 --> 00:01:20.850
But it doesn't have
a direction.

00:01:20.850 --> 00:01:23.470
We're not going at
an angle in time.

00:01:23.470 --> 00:01:25.120
So we could take the scalar
quantity out.

00:01:25.120 --> 00:01:27.110
It doesn't affect this
vector cross product.

00:01:27.110 --> 00:01:32.440
So what we get left with is,
force is equal to charge per

00:01:32.440 --> 00:01:36.250
time times-- and this is just a
regular times, because this

00:01:36.250 --> 00:01:39.010
is just a number, it's not a
vector-- times the cross

00:01:39.010 --> 00:01:46.420
product of the distance vector
and the magnetic field.

00:01:46.420 --> 00:01:49.840
And what is charge per time?

00:01:49.840 --> 00:01:51.350
Coulombs per second?

00:01:51.350 --> 00:01:52.770
Well, that's just current.

00:01:52.770 --> 00:02:00.790
So we get that force is equal to
current times the distance

00:02:00.790 --> 00:02:08.199
that the current is flowing
along, taken-- and you take

00:02:08.199 --> 00:02:11.930
the cross product of that
with the magnetic field.

00:02:11.930 --> 00:02:14.160
And sometimes this is written as
a capital L because it's a

00:02:14.160 --> 00:02:16.940
vector and all that, but we
started with a lower case l,

00:02:16.940 --> 00:02:18.660
so we'll stay with
the lower case l.

00:02:18.660 --> 00:02:21.750
So let's see if we can apply
this formula, which is really

00:02:21.750 --> 00:02:22.580
the same thing as this.

00:02:22.580 --> 00:02:25.800
We just took the division by
time and took it out of

00:02:25.800 --> 00:02:27.380
velocity so we get distance.

00:02:27.380 --> 00:02:30.660
And we took it and we divided
the coulombs, or we took the

00:02:30.660 --> 00:02:32.070
charge divided by that.

00:02:32.070 --> 00:02:36.470
So we took charge divided by
time, or charge per unit of

00:02:36.470 --> 00:02:37.770
time, you get current.

00:02:37.770 --> 00:02:42.000
So this is really just another
way of writing this.

00:02:42.000 --> 00:02:43.710
It's not even a new formula.

00:02:43.710 --> 00:02:45.100
You could almost prove
it to yourself if

00:02:45.100 --> 00:02:46.510
you ever forget it.

00:02:46.510 --> 00:02:52.420
But let's see if we can use this
to figure out the effect

00:02:52.420 --> 00:02:56.330
that a magnetic field has on
a current carrying wire.

00:02:56.330 --> 00:02:58.520
So let me-- actually, I probably
want to put this up

00:02:58.520 --> 00:03:02.550
at the top, just so that I have
space to draw a current

00:03:02.550 --> 00:03:03.355
carrying wire.

00:03:03.355 --> 00:03:05.640
So let me rewrite it in green.

00:03:05.640 --> 00:03:09.220
So you're familiar with the
formula in all colors.

00:03:09.220 --> 00:03:13.680
So now our new derivation is
that the force of a magnetic

00:03:13.680 --> 00:03:19.280
field on a current carrying wire
is equal to the current

00:03:19.280 --> 00:03:22.770
in the wire-- and that's just a
scalar quantity, although it

00:03:22.770 --> 00:03:25.760
could be positive or negative
depending on the direction.

00:03:25.760 --> 00:03:29.400
Well, current is always a
positive number, but if this

00:03:29.400 --> 00:03:31.650
current is going in the opposite
direction as our

00:03:31.650 --> 00:03:33.040
distance vector, then it
might be negative.

00:03:33.040 --> 00:03:34.810
But I wouldn't worry
about that for now.

00:03:34.810 --> 00:03:37.530
Let's just assume this is a
current in the direction of

00:03:37.530 --> 00:03:39.080
the distance vector.

00:03:39.080 --> 00:03:43.210
So it's a scalar quantity
current times our distance

00:03:43.210 --> 00:03:47.200
vector l, or maybe the length
of the conductor.

00:03:47.200 --> 00:03:49.650
You take the cross product
of l with the

00:03:49.650 --> 00:03:52.980
magnetic field vector.

00:03:52.980 --> 00:03:54.360
So let's see if we
can apply that.

00:03:54.360 --> 00:03:57.430
Let's say that we have a wire.

00:03:57.430 --> 00:04:02.070
Actually, let's do the magnetic
field first. I've

00:04:02.070 --> 00:04:03.130
been doing a lot of magnetic
fields that

00:04:03.130 --> 00:04:04.490
pop out of the screen.

00:04:04.490 --> 00:04:07.810
Let's do a magnetic field that
goes into the screen.

00:04:07.810 --> 00:04:09.310
And those are even
easier to draw.

00:04:09.310 --> 00:04:11.080
They're just x's.

00:04:11.080 --> 00:04:12.550
Now, why is it an x?

00:04:12.550 --> 00:04:16.750
Because you're looking at the
rear end of an arrow.

00:04:16.750 --> 00:04:17.720
That's why it's an x.

00:04:17.720 --> 00:04:21.740
And that's why a circle with a
dot means a field or a vector

00:04:21.740 --> 00:04:24.420
coming out of the window.

00:04:24.420 --> 00:04:27.750
Because if an arrow was shot at
you, all you would see is

00:04:27.750 --> 00:04:30.350
the tip of the arrow
with maybe a little

00:04:30.350 --> 00:04:31.140
circle around it.

00:04:31.140 --> 00:04:34.160
But anyway, this shows us a
vector going into the screen.

00:04:34.160 --> 00:04:36.430
So this is our magnetic field.

00:04:36.430 --> 00:04:38.970
That is B.

00:04:38.970 --> 00:04:40.620
I don't know, let's
assign some value.

00:04:40.620 --> 00:04:49.200
Let's say that the magnitude
of B is equal to 1 tesla.

00:04:49.200 --> 00:04:53.140
And let's say I have a
wire going through

00:04:53.140 --> 00:04:56.300
that magnetic field.

00:04:56.300 --> 00:05:04.400
Let's say the wire is going
along or it's in the plane of

00:05:04.400 --> 00:05:06.800
your computer monitor.

00:05:06.800 --> 00:05:15.280
Let me just draw a wire going
through the magnetic field.

00:05:15.280 --> 00:05:18.210
And my question to you-- let
me tell you a little bit of

00:05:18.210 --> 00:05:20.620
information about this wire.

00:05:20.620 --> 00:05:24.050
Let's say the wire is
carrying a current.

00:05:24.050 --> 00:05:27.670
So I is going in
that direction.

00:05:27.670 --> 00:05:32.410
And it is carrying a current
of-- I'm just making up

00:05:32.410 --> 00:05:38.330
numbers-- 5 amperes, or
5 coulombs per second.

00:05:38.330 --> 00:05:44.060
My question to you is, what is
the net force of this magnetic

00:05:44.060 --> 00:05:47.550
field on a section
of this wire?

00:05:47.550 --> 00:05:50.370
And let's make this section of
the wire, I don't know, let's

00:05:50.370 --> 00:05:53.190
say it's a 2 meter
section of wire.

00:05:56.890 --> 00:06:00.720
So obviously the more wire you
have, the more charged moving

00:06:00.720 --> 00:06:03.390
particles you'll have. So the
larger a section you have, the

00:06:03.390 --> 00:06:06.960
more of a force you'll have on
that longer piece of wire.

00:06:06.960 --> 00:06:08.540
So we have to pick our length.

00:06:08.540 --> 00:06:10.610
So we want to know, what is
the force of the magnetic

00:06:10.610 --> 00:06:12.970
field on this section of wire?

00:06:12.970 --> 00:06:16.590
From here to here.

00:06:16.590 --> 00:06:17.910
So let's just go to
this formula.

00:06:17.910 --> 00:06:20.200
The force is equal
to the current.

00:06:20.200 --> 00:06:21.760
So that's 5 amperes.

00:06:21.760 --> 00:06:24.320
And remember, just from what we
learned about electricity,

00:06:24.320 --> 00:06:28.390
the current is the direction
that notional positive charges

00:06:28.390 --> 00:06:30.090
would travel in, and
suits us fine.

00:06:30.090 --> 00:06:33.830
Because when we did the first
equation, we cared about the

00:06:33.830 --> 00:06:35.360
direction a positive
charge would go in.

00:06:35.360 --> 00:06:37.770
And if it was an electron or a
negative charge, we would put

00:06:37.770 --> 00:06:38.630
a negative sign there.

00:06:38.630 --> 00:06:39.570
So that works fine.

00:06:39.570 --> 00:06:41.850
But if you ever have to
visualize things as they maybe

00:06:41.850 --> 00:06:44.260
are in reality, but when you
talk about electrons it's hard

00:06:44.260 --> 00:06:46.130
to say that they really are
reality, because they're

00:06:46.130 --> 00:06:48.310
almost more an idea
than an object.

00:06:48.310 --> 00:06:50.760
But it's always good to remember
that when the current

00:06:50.760 --> 00:06:53.170
is flowing in this direction,
that would be true.

00:06:53.170 --> 00:06:55.820
Because if they were positive
charges moving, but we know

00:06:55.820 --> 00:06:59.150
it's a negative charge moving
in the opposite direction.

00:06:59.150 --> 00:07:01.960
Or you can think of it
as, maybe, holes.

00:07:01.960 --> 00:07:03.490
Well, I don't want
to get into that.

00:07:03.490 --> 00:07:07.130
But anyway, the current-- you
could visualize it if you like

00:07:07.130 --> 00:07:08.770
as positive charges going
in this direction.

00:07:08.770 --> 00:07:10.650
So the current is going
this direction.

00:07:10.650 --> 00:07:13.170
So you could view this
distance vector

00:07:13.170 --> 00:07:15.490
that we care about.

00:07:15.490 --> 00:07:17.670
Its magnitude is 2 meters.

00:07:17.670 --> 00:07:19.990
Because that's the length
of wire in question.

00:07:19.990 --> 00:07:22.700
And its direction is the
direction of the current.

00:07:22.700 --> 00:07:27.110
So let me-- this is l.

00:07:27.110 --> 00:07:30.990
Sometimes I get a little carried
away on tangents.

00:07:30.990 --> 00:07:32.280
So that is l.

00:07:35.530 --> 00:07:38.100
It's 2 meters in
that direction.

00:07:38.100 --> 00:07:39.660
I is 5 amperes.

00:07:39.660 --> 00:07:42.050
And we already figured
out that the

00:07:42.050 --> 00:07:44.910
magnetic field is 1 tesla.

00:07:44.910 --> 00:07:46.950
So what's this going
to be equal to?

00:07:46.950 --> 00:07:52.180
So the force is going to be
equal to-- we're using all SI

00:07:52.180 --> 00:07:57.110
units, so we don't have to
convert anything-- 5 amperes

00:07:57.110 --> 00:08:02.840
times 2 meters in
that direction.

00:08:02.840 --> 00:08:05.030
I won't specify right now,
let's just say that's a

00:08:05.030 --> 00:08:07.540
magnitude of l.

00:08:07.540 --> 00:08:08.530
Actually, let me write it.

00:08:08.530 --> 00:08:18.220
Well, 2 meters times the
magnetic field, 1 tesla.

00:08:18.220 --> 00:08:20.350
And so when you take a cross
product of something, this is

00:08:20.350 --> 00:08:21.290
just a reminder.

00:08:21.290 --> 00:08:22.050
l cross B.

00:08:22.050 --> 00:08:29.130
That's equal to the magnitude of
l times the magnitude of B

00:08:29.130 --> 00:08:35.700
times the sine of the angle
between them times some unit

00:08:35.700 --> 00:08:37.299
directional vector that
we figure out with

00:08:37.299 --> 00:08:38.480
the right hand rule.

00:08:38.480 --> 00:08:40.870
So we already did
the magnitude of

00:08:40.870 --> 00:08:41.580
the distance vector.

00:08:41.580 --> 00:08:42.460
That was 2 meters.

00:08:42.460 --> 00:08:45.590
We did the magnitude of
the magnetic field.

00:08:45.590 --> 00:08:47.910
And what's the sine of the
angle between them?

00:08:47.910 --> 00:08:51.970
Well, if the magnetic field is
going into the screen, if it's

00:08:51.970 --> 00:08:53.690
going straight into the screen,
you could imagine a

00:08:53.690 --> 00:08:55.550
bunch of arrows shooting
into the screen.

00:08:55.550 --> 00:08:56.930
Those are the vectors.

00:08:56.930 --> 00:09:02.990
While our distance vector, or
this l is in the screen, they

00:09:02.990 --> 00:09:04.980
actually are perpendicular,
in 3 dimensions.

00:09:04.980 --> 00:09:06.580
So this angle is 90 degrees.

00:09:06.580 --> 00:09:09.400
So this actually
just becomes 1.

00:09:09.400 --> 00:09:11.280
So in terms of the magnitude,
we're done.

00:09:11.280 --> 00:09:15.250
The l cross B magnitude
is 2 times 1 tesla.

00:09:15.250 --> 00:09:17.030
And then we multiply that
times the current.

00:09:17.030 --> 00:09:19.360
And then we actually have the
magnitude of the force.

00:09:19.360 --> 00:09:23.900
The magnitude of this force is
going to be equal to 5 amperes

00:09:23.900 --> 00:09:26.570
times 2 meters times 1 tesla.

00:09:26.570 --> 00:09:30.090
Which is equal to 10 newtons.

00:09:30.090 --> 00:09:32.980
And then the only question left
is, what is the direction

00:09:32.980 --> 00:09:35.400
of the force that the magnetic
field is exerting?

00:09:35.400 --> 00:09:38.360
And this is where we break
out the right hand rule.

00:09:38.360 --> 00:09:39.220
And it's no different.

00:09:39.220 --> 00:09:44.980
You could just imagine one of
the positive particles moving

00:09:44.980 --> 00:09:46.950
in that direction, and just
use the right hand rule.

00:09:46.950 --> 00:09:50.450
So let's take our hand out.

00:09:50.450 --> 00:09:52.670
And if we-- let me
draw a hand.

00:09:52.670 --> 00:09:54.840
A right hand.

00:09:54.840 --> 00:09:58.400
So this is my right hand.

00:09:58.400 --> 00:10:00.500
If I have my thumb sticking
out like that.

00:10:00.500 --> 00:10:03.550
So the l is going to
be my index finger.

00:10:03.550 --> 00:10:05.910
The first thing in the
cross product.

00:10:05.910 --> 00:10:08.610
And then the B is the
magnetic field.

00:10:08.610 --> 00:10:09.980
That's going into the screen.

00:10:09.980 --> 00:10:11.210
So you can't see it.

00:10:11.210 --> 00:10:13.710
All you can take my word for it
is that my middle finger is

00:10:13.710 --> 00:10:16.390
pointed downwards into the
screen and then my other

00:10:16.390 --> 00:10:18.700
fingers are just doing
something else.

00:10:18.700 --> 00:10:20.100
And there you have it.

00:10:20.100 --> 00:10:22.760
Your thumb is actually the
direction of the force.

00:10:25.450 --> 00:10:31.150
Your index finger is the
direction of-- we'll say l for

00:10:31.150 --> 00:10:32.180
these purposes.

00:10:32.180 --> 00:10:34.430
And then the magnetic field is
going into it, so you can't

00:10:34.430 --> 00:10:36.250
see my middle finger but it's
pointing downwards.

00:10:36.250 --> 00:10:38.780
I could draw a little x there,
to show it's going downwards.

00:10:38.780 --> 00:10:41.100
And then the force is what
my thumb is doing.

00:10:41.100 --> 00:10:44.400
So the force on this wire, or
at least on that section of

00:10:44.400 --> 00:10:47.630
wire, is going to be
perpendicular to the direction

00:10:47.630 --> 00:10:48.830
of the current.

00:10:48.830 --> 00:10:52.290
And that direction is going
to be a 10 newton force.

00:10:52.290 --> 00:10:54.790
Anyway, I've run out of time.


Magnetic force on a proton example (part 1)

WEBVTT
Kind: captions
Language: en

00:00:01.010 --> 00:00:03.950
In the last video we learned--
or at least I showed you, I

00:00:03.950 --> 00:00:05.580
don't know if you've learned it
yet, but we'll learn it in

00:00:05.580 --> 00:00:05.890
this video.

00:00:05.890 --> 00:00:09.010
But we learned that the force
on a moving charge from a

00:00:09.010 --> 00:00:12.020
magnetic field, and it's a
vector quantity, is equal to

00:00:12.020 --> 00:00:16.320
the charge-- on the moving
charge-- times the cross

00:00:16.320 --> 00:00:23.260
product of the velocity of the
charge and the magnetic field.

00:00:23.260 --> 00:00:28.720
And we use this to show you that
the units of a magnetic

00:00:28.720 --> 00:00:32.880
field-- this is not a beta, it's
a B-- but the units of a

00:00:32.880 --> 00:00:37.300
magnetic field are the tesla--
which is abbreviated with a

00:00:37.300 --> 00:00:41.380
capital T-- and that
is equal to newton

00:00:41.380 --> 00:00:46.000
seconds per coulomb meters.

00:00:46.000 --> 00:00:49.520
So let's see if we can apply
that to an actual problem.

00:00:49.520 --> 00:00:53.525
So let's say that I have a
magnetic field, and let's say

00:00:53.525 --> 00:00:55.630
it's popping out
of the screen.

00:00:55.630 --> 00:00:57.440
I'm making this up on the
fly, so I hope the

00:00:57.440 --> 00:00:58.960
numbers turn out.

00:00:58.960 --> 00:01:01.860
It's inspired by a problem that
I read in Barron's AP

00:01:01.860 --> 00:01:03.380
calculus book.

00:01:03.380 --> 00:01:06.710
So if I want to draw a bunch of
vectors or a vector field

00:01:06.710 --> 00:01:08.400
that's popping out of the
screen, I could just do the

00:01:08.400 --> 00:01:10.300
top of the arrowheads.

00:01:10.300 --> 00:01:14.580
I'll draw them in magenta.

00:01:14.580 --> 00:01:17.230
So let's say I have
a vector field.

00:01:17.230 --> 00:01:18.810
So you can imagine
a bunch of arrows

00:01:18.810 --> 00:01:21.420
popping out of the screen.

00:01:21.420 --> 00:01:24.600
I'll just draw a couple of them
just so you get the sense

00:01:24.600 --> 00:01:25.790
that it's a field.

00:01:25.790 --> 00:01:29.050
It pervades the space.

00:01:29.050 --> 00:01:32.390
These are a bunch of
arrows popping out.

00:01:32.390 --> 00:01:35.320
And the field is popping out.

00:01:35.320 --> 00:01:38.650
And the magnitude of the field,
let's say it is, I

00:01:38.650 --> 00:01:44.170
don't know, let's say
it is 0.5 teslas.

00:01:44.170 --> 00:01:47.530
Let's say I have some proton
that comes speeding along.

00:01:52.190 --> 00:01:57.130
And it's speeding along at a
velocity-- so the velocity of

00:01:57.130 --> 00:02:04.350
the proton is equal to
6 times 10 to the

00:02:04.350 --> 00:02:07.960
seventh meters per second.

00:02:07.960 --> 00:02:13.590
And that is actually about 1/5
of the velocity or 1/5 of the

00:02:13.590 --> 00:02:14.340
speed of light.

00:02:14.340 --> 00:02:18.060
So we're pretty much in the
relativistic realm, but we

00:02:18.060 --> 00:02:20.180
won't go too much into
relativity because then the

00:02:20.180 --> 00:02:21.910
mass of the proton increases,
et cetera, et cetera.

00:02:21.910 --> 00:02:25.250
We just assume that the mass
hasn't increased significantly

00:02:25.250 --> 00:02:26.020
at this point.

00:02:26.020 --> 00:02:28.970
So we have this proton going at
a 1/5 of the speed of light

00:02:28.970 --> 00:02:32.040
and it's crossing through
this magnetic field.

00:02:32.040 --> 00:02:37.340
So the first question is what is
the magnitude and direction

00:02:37.340 --> 00:02:41.980
of the force on this proton
from this magnetic field?

00:02:41.980 --> 00:02:45.280
Well, let's figure out the
magnitude first. So how can we

00:02:45.280 --> 00:02:47.320
figure out the magnitude?

00:02:47.320 --> 00:02:52.100
Well, first of all, what is
the charge on a proton?

00:02:52.100 --> 00:02:54.170
Well, we don't know it right
now, but my calculator has

00:02:54.170 --> 00:02:54.710
that stored in it.

00:02:54.710 --> 00:02:57.970
And if you have a TI graphing
calculator, your calculator

00:02:57.970 --> 00:02:59.300
would also have it
stored in it.

00:02:59.300 --> 00:03:02.330
So let's just write that down
as a variable right now.

00:03:02.330 --> 00:03:07.520
So the magnitude of the force on
the particle is going to be

00:03:07.520 --> 00:03:13.110
equal to the charge of a
proton-- I'll call it Q sub

00:03:13.110 --> 00:03:20.740
p-- times the magnitude of the
velocity, 6 times 10 to the

00:03:20.740 --> 00:03:22.150
seventh meters per second.

00:03:22.150 --> 00:03:23.070
We're using all the
right units.

00:03:23.070 --> 00:03:24.560
If this was centimeters
we'd probably want to

00:03:24.560 --> 00:03:27.020
convert it to meters.

00:03:27.020 --> 00:03:28.970
6 times 10 to the seventh
meters per second.

00:03:28.970 --> 00:03:35.040
And then times the magnitude of
the magnetic field, which

00:03:35.040 --> 00:03:38.590
is 0.5 soon. teslas-- I didn't
have to write the units there,

00:03:38.590 --> 00:03:41.200
but I'll do it there--
times sine of the

00:03:41.200 --> 00:03:43.510
angle between them.

00:03:43.510 --> 00:03:46.480
I'll write that down
right now.

00:03:46.480 --> 00:03:47.770
But let me ask you a question.

00:03:47.770 --> 00:03:51.650
If the magnetic field is
pointing straight out of the

00:03:51.650 --> 00:03:53.760
screen-- and you're going to
have to do a little bit of

00:03:53.760 --> 00:03:57.320
three-dimensional visualization
now-- and this

00:03:57.320 --> 00:04:01.000
particle is moving in the plane
of the field, what is

00:04:01.000 --> 00:04:02.950
the angle between them?

00:04:02.950 --> 00:04:06.280
If you visualize it in three
dimensions, they're actually

00:04:06.280 --> 00:04:07.410
orthogonal to each other.

00:04:07.410 --> 00:04:09.590
They're at right angles
to each other.

00:04:09.590 --> 00:04:12.280
Because these vectors are
popping out of the screen.

00:04:12.280 --> 00:04:16.630
They are perpendicular to the
plane that defines the screen,

00:04:16.630 --> 00:04:20.459
while this proton is moving
within this plane.

00:04:20.459 --> 00:04:23.050
So the angle between them, if
you can visualize it in three

00:04:23.050 --> 00:04:25.530
dimensions, is 90 degrees.

00:04:25.530 --> 00:04:27.470
Or they're perfectly
perpendicular.

00:04:27.470 --> 00:04:29.660
And when things are perfectly
perpendicular, what is the

00:04:29.660 --> 00:04:31.040
sine of 90 degrees?

00:04:31.040 --> 00:04:33.040
Or the sine of pi over 2?

00:04:33.040 --> 00:04:35.330
Either way, if you want
to deal in radians.

00:04:35.330 --> 00:04:37.680
Well, it's just equal to 1.

00:04:37.680 --> 00:04:40.690
The whole-- hopefully--
intuition you got about the

00:04:40.690 --> 00:04:43.990
cross product is we only want to
multiply the components of

00:04:43.990 --> 00:04:46.580
the two vectors that are
perpendicular to each other.

00:04:46.580 --> 00:04:48.110
And that's why we have
the sine of theta.

00:04:48.110 --> 00:04:51.310
But if the entire vectors are
perpendicular to each other,

00:04:51.310 --> 00:04:54.130
then we just multiply the
magnitude of the vector.

00:04:54.130 --> 00:04:55.910
Or if you even forget to do
that, you say, oh well,

00:04:55.910 --> 00:04:56.930
they're perpendicular.

00:04:56.930 --> 00:04:57.900
They're at 90 degree angles.

00:04:57.900 --> 00:04:58.870
Sine of 90 degrees?

00:04:58.870 --> 00:05:00.470
Well, that's just 1.

00:05:00.470 --> 00:05:03.300
So this is just 1.

00:05:03.300 --> 00:05:06.900
So the magnitude of the force
is actually pretty easy to

00:05:06.900 --> 00:05:08.990
calculate, if we know the
charge on a proton.

00:05:08.990 --> 00:05:12.410
And let's see if we can figure
out the charge on a proton.

00:05:12.410 --> 00:05:17.490
Let me get the trusty
TI-85 out.

00:05:17.490 --> 00:05:19.780
Let me clear there,
just so you can

00:05:19.780 --> 00:05:23.460
appreciate the TI-85 store.

00:05:23.460 --> 00:05:26.400
If you press second and
constant-- that's second and

00:05:26.400 --> 00:05:27.330
then the number 4.

00:05:27.330 --> 00:05:29.950
They have a little constant
above it.

00:05:29.950 --> 00:05:32.840
You get their constant
functions.

00:05:32.840 --> 00:05:33.590
Or their values.

00:05:33.590 --> 00:05:35.590
And you say the built-in--
I care about the built-in

00:05:35.590 --> 00:05:37.900
functions, so let me press F1.

00:05:37.900 --> 00:05:39.780
And they have a bunch of-- you
know, this is Avogadro's

00:05:39.780 --> 00:05:43.760
number, they have a bunch of
interesting-- this is the

00:05:43.760 --> 00:05:45.320
charge of an electron.

00:05:45.320 --> 00:05:46.540
Which is actually the
same thing as

00:05:46.540 --> 00:05:47.420
the charge of a proton.

00:05:47.420 --> 00:05:48.670
So let's use that.

00:05:50.980 --> 00:05:53.380
Electrons-- just remember--
electrons and protons have

00:05:53.380 --> 00:05:54.210
offsetting charges.

00:05:54.210 --> 00:05:56.380
One's positive and
one's negative.

00:05:56.380 --> 00:05:59.050
It's just that a proton
is more massive.

00:05:59.050 --> 00:05:59.880
That's how they're different.

00:05:59.880 --> 00:06:01.020
And of course, it's positive.

00:06:01.020 --> 00:06:05.270
Let's just confirm that that's
the charge of an electron.

00:06:05.270 --> 00:06:06.690
But that's also the charge
of a proton.

00:06:06.690 --> 00:06:07.830
And actually, this positive
value is the

00:06:07.830 --> 00:06:09.240
exact charge of a proton.

00:06:09.240 --> 00:06:11.670
They should have maybe put a
negative number here, but all

00:06:11.670 --> 00:06:13.180
we care about is the value.

00:06:13.180 --> 00:06:14.920
So let's use that again.

00:06:14.920 --> 00:06:17.040
The charge of an electron-- and
it is positive, so that's

00:06:17.040 --> 00:06:23.280
the same thing as the charge for
a proton-- times 6 times

00:06:23.280 --> 00:06:28.290
10 to the seventh-- 6 E 7, you
just press that EE button on

00:06:28.290 --> 00:06:30.790
your calculator-- times
0.5 teslas.

00:06:33.480 --> 00:06:37.440
Make sure all your units are
in teslas, meters, and

00:06:37.440 --> 00:06:41.380
coulombs, and then your result
will be in newtons.

00:06:41.380 --> 00:06:49.630
And you get 4.8 times 10 to
the negative 12 newtons.

00:06:49.630 --> 00:06:50.950
Let me write that down.

00:06:50.950 --> 00:07:03.150
So the magnitude of this force
is equal to 4.8 times 10 to

00:07:03.150 --> 00:07:05.610
the minus 12 newtons.

00:07:05.610 --> 00:07:06.950
So that's the magnitude.

00:07:06.950 --> 00:07:08.760
Now what is the direction?

00:07:08.760 --> 00:07:10.440
What is the direction
of this force?

00:07:10.440 --> 00:07:12.750
Well, this you is where we break
out-- we put our pens

00:07:12.750 --> 00:07:16.480
down if we're right handed, and
we use our right hand rule

00:07:16.480 --> 00:07:17.950
to figure out the direction.

00:07:17.950 --> 00:07:18.820
So what do we have to do?

00:07:18.820 --> 00:07:22.460
So when you take something
crossed something, the first

00:07:22.460 --> 00:07:25.880
thing in the cross product is
your index finger on your

00:07:25.880 --> 00:07:29.000
right hand.

00:07:29.000 --> 00:07:33.315
And then the second thing is
your middle finger pointed at

00:07:33.315 --> 00:07:35.570
a right angle with your
index finger.

00:07:35.570 --> 00:07:36.930
Let's see if I can do this.

00:07:36.930 --> 00:07:41.100
So I want my index finger
on my right hand to

00:07:41.100 --> 00:07:42.930
point to the right.

00:07:42.930 --> 00:07:46.070
But I want my middle finger
to point upwards.

00:07:46.070 --> 00:07:49.780
Let me see if I can
pull that off.

00:07:49.780 --> 00:07:54.220
So my right hand is going to
look something like this.

00:07:54.220 --> 00:07:55.470
And my hand is brown.

00:07:58.070 --> 00:08:00.260
So my right hand is going to
look something like this.

00:08:00.260 --> 00:08:05.780
My index finger is pointing in
the direction of the velocity

00:08:05.780 --> 00:08:10.990
vector, while my middle finger
is pointing the direction of

00:08:10.990 --> 00:08:12.720
the magnetic field.

00:08:12.720 --> 00:08:17.030
So my index finger is going to
point straight up, so all you

00:08:17.030 --> 00:08:18.510
see is the tip of it.

00:08:18.510 --> 00:08:23.860
And then my other fingers are
just going to go like that.

00:08:23.860 --> 00:08:25.710
And then my thumb is
going to do what?

00:08:25.710 --> 00:08:29.850
My thumb is going-- this is the
heel of my thumb-- and so

00:08:29.850 --> 00:08:31.770
my thumb is going to be at a
right angle to both of them.

00:08:31.770 --> 00:08:35.470
So my thumb points
down like this.

00:08:35.470 --> 00:08:36.909
This is often the
hardest part.

00:08:36.909 --> 00:08:40.390
Just making sure you get your
hand visualization right with

00:08:40.390 --> 00:08:41.970
the cross product.

00:08:41.970 --> 00:08:47.680
So just as a review, this
is the direction of v.

00:08:47.680 --> 00:08:50.990
This is the direction of
the magnetic field.

00:08:50.990 --> 00:08:52.670
It's popping out.

00:08:52.670 --> 00:08:55.830
And so if I arrange my right
hand like that, my thumb

00:08:55.830 --> 00:08:57.330
points down.

00:08:57.330 --> 00:09:00.560
So this is the direction
of the force.

00:09:00.560 --> 00:09:04.860
So as this particle moves to the
right with some velocity,

00:09:04.860 --> 00:09:08.120
there's actually going to
be a downward force.

00:09:08.120 --> 00:09:09.950
Downward on this plane.

00:09:09.950 --> 00:09:13.110
So the force is going to
move in this direction.

00:09:13.110 --> 00:09:14.730
So what's going to happen?

00:09:14.730 --> 00:09:16.900
Well, what happens-- if you
remember a little bit about

00:09:16.900 --> 00:09:19.620
your circular motion and your
centripetal acceleration and

00:09:19.620 --> 00:09:23.620
all that-- what happens when you
have a force perpendicular

00:09:23.620 --> 00:09:25.060
to velocity?

00:09:25.060 --> 00:09:25.720
Well, think about it.

00:09:25.720 --> 00:09:27.490
If you have a force here and the
velocity is like that, if

00:09:27.490 --> 00:09:29.550
the particles-- it'll
be deflected a

00:09:29.550 --> 00:09:30.460
little bit to the right.

00:09:30.460 --> 00:09:32.820
And then since the force
is always going to be

00:09:32.820 --> 00:09:35.030
perpendicular to the velocity
vector, the force is going to

00:09:35.030 --> 00:09:36.080
charge like that.

00:09:36.080 --> 00:09:40.420
So the particle is actually
going to go in a circle.

00:09:40.420 --> 00:09:43.750
As long as it's in the magnetic
field, the force

00:09:43.750 --> 00:09:48.120
applied to the particle by the
magnetic field is going to be

00:09:48.120 --> 00:09:51.300
perpendicular to the velocity
of the particle.

00:09:51.300 --> 00:09:53.150
So the velocity of the
particle-- so it's going to

00:09:53.150 --> 00:09:55.660
actually be like a centripetal
force on the particle.

00:09:55.660 --> 00:09:58.530
So the particle is going
to go into a circle.

00:09:58.530 --> 00:10:01.150
And in the next video we'll
actually figure out the radius

00:10:01.150 --> 00:10:02.140
of that circle.

00:10:02.140 --> 00:10:05.500
And just one thing I want
to let you think about.

00:10:05.500 --> 00:10:13.370
It's kind of weird or spooky
to me that the force on a

00:10:13.370 --> 00:10:16.660
moving particle-- it doesn't
matter about

00:10:16.660 --> 00:10:18.710
the particle's mass.

00:10:18.710 --> 00:10:22.500
It just matters the particle's
velocity and charge.

00:10:22.500 --> 00:10:25.840
So it's kind of a strange
phenomenon that the faster you

00:10:25.840 --> 00:10:28.600
move through a magnetic field--
or at least if you're

00:10:28.600 --> 00:10:30.850
charged, if you're a charged
particle-- the faster you move

00:10:30.850 --> 00:10:33.560
through a magnetic field, the
more force that magnetic field

00:10:33.560 --> 00:10:35.230
is going to apply to you.

00:10:35.230 --> 00:10:36.950
It seems a little bit, you know,
how does that magnetic

00:10:36.950 --> 00:10:38.420
field know how fast
you're moving?

00:10:38.420 --> 00:10:40.030
But anyway, I'll leave
you with that.

00:10:40.030 --> 00:10:43.530
In the next video we'll
explore this magnetic

00:10:43.530 --> 00:10:45.560
phenomenon a little bit deeper.

00:10:45.560 --> 00:10:46.810
See


Magnetic force on a charge

WEBVTT
Kind: captions
Language: en

00:00:00.840 --> 00:00:03.450
We know a little bit
about magnets now.

00:00:03.450 --> 00:00:06.020
Let's see if we can study it
further and learn a little bit

00:00:06.020 --> 00:00:08.880
about magnetic field and
actually the effects that they

00:00:08.880 --> 00:00:10.960
have on moving charges.

00:00:10.960 --> 00:00:13.650
And that's actually really how
we define magnetic field.

00:00:13.650 --> 00:00:17.910
So first of all, with any field
it's good to have a way

00:00:17.910 --> 00:00:19.730
to visualize it.

00:00:19.730 --> 00:00:24.270
With the electrostatic fields
we drew field lines.

00:00:24.270 --> 00:00:26.910
So let's try to do the same
thing with magnetic fields.

00:00:26.910 --> 00:00:29.650
Let's say this is
my bar magnet.

00:00:29.650 --> 00:00:34.020
This is the north pole and
this is the south pole.

00:00:34.020 --> 00:00:36.940
Now the convention, when we're
drawing magnetic field lines,

00:00:36.940 --> 00:00:39.410
is to always start at the north
pole and go towards the

00:00:39.410 --> 00:00:40.180
south pole.

00:00:40.180 --> 00:00:44.470
And you can almost view it as
the path that a magnetic north

00:00:44.470 --> 00:00:46.000
monopole would take.

00:00:46.000 --> 00:00:48.490
So if it starts here-- if a
magnetic north monopole, even

00:00:48.490 --> 00:00:50.650
though as far as we know they
don't exist in nature,

00:00:50.650 --> 00:00:53.060
although they theoretically
could, but let's just say for

00:00:53.060 --> 00:00:54.800
the sake of argument
that we do have a

00:00:54.800 --> 00:00:55.950
magnetic north monopole.

00:00:55.950 --> 00:00:57.950
If it started out here, it would
want to run away from

00:00:57.950 --> 00:01:01.040
this north pole and would try
to get to the south pole.

00:01:01.040 --> 00:01:02.940
So it would do something,
its path would look

00:01:02.940 --> 00:01:04.190
something like this.

00:01:07.370 --> 00:01:09.110
If it started here, maybe
its path would look

00:01:09.110 --> 00:01:10.360
something like this.

00:01:12.650 --> 00:01:14.460
Or if it started here, maybe
its path would look

00:01:14.460 --> 00:01:15.240
something like this.

00:01:15.240 --> 00:01:18.280
I think you get the point.

00:01:18.280 --> 00:01:21.500
Another way to visualize it is
instead of thinking about a

00:01:21.500 --> 00:01:24.610
magnetic north monopole and the
path it would take, you

00:01:24.610 --> 00:01:28.800
could think of, well, what if
I had a little compass here?

00:01:28.800 --> 00:01:31.290
Let me draw it in a
different color.

00:01:31.290 --> 00:01:35.140
Let's say I put the
compass here.

00:01:35.140 --> 00:01:36.625
That's not where I
want to do it.

00:01:36.625 --> 00:01:38.430
Let's say I do it here.

00:01:38.430 --> 00:01:42.110
The compass pointer will
actually be tangent to the

00:01:42.110 --> 00:01:43.310
field line.

00:01:43.310 --> 00:01:45.560
So the pointer could
look something like

00:01:45.560 --> 00:01:47.712
this at this point.

00:01:47.712 --> 00:01:50.150
It would look something
like this.

00:01:50.150 --> 00:01:53.460
And this would be the north pole
of the pointer and this

00:01:53.460 --> 00:01:55.440
would be the south pole
of the pointer.

00:01:55.440 --> 00:01:57.740
Or you could-- that's how north
and south were defined.

00:01:57.740 --> 00:01:59.940
People had compasses, they said,
oh, this is the north

00:01:59.940 --> 00:02:04.100
seeking pole, and it points
in that direction.

00:02:04.100 --> 00:02:05.740
But it's actually seeking
the south pole

00:02:05.740 --> 00:02:06.580
of the larger magnet.

00:02:06.580 --> 00:02:08.949
And that's where we got into
that big confusing discussion

00:02:08.949 --> 00:02:12.980
of that the magnetic geographic
north pole that

00:02:12.980 --> 00:02:16.840
we're used to is actually the
south pole of the magnet that

00:02:16.840 --> 00:02:17.340
we call Earth.

00:02:17.340 --> 00:02:19.800
And you could view the last
video on Introduction to

00:02:19.800 --> 00:02:22.160
Magnetism to get confused
about that.

00:02:22.160 --> 00:02:23.190
But I think you see
what I'm saying.

00:02:23.190 --> 00:02:26.100
North always seeks south the
same way that positive seeks

00:02:26.100 --> 00:02:27.430
negative, and vice versa.

00:02:27.430 --> 00:02:29.870
And north runs away
from north.

00:02:29.870 --> 00:02:33.060
And really the main conceptual
difference-- although they are

00:02:33.060 --> 00:02:36.530
kind of very different
properties-- although we will

00:02:36.530 --> 00:02:39.830
see later they actually end up
being the same thing, that we

00:02:39.830 --> 00:02:41.800
have something called an
electromagnetic force, once we

00:02:41.800 --> 00:02:43.680
start learning about Maxwell's
equations and

00:02:43.680 --> 00:02:44.520
relativity and all that.

00:02:44.520 --> 00:02:46.030
But we don't have to worry
about that right now.

00:02:46.030 --> 00:02:50.090
But in classical electricity and
magnetism, they're kind of

00:02:50.090 --> 00:02:51.660
a different force.

00:02:51.660 --> 00:02:54.070
And the main difference--
although you know, these field

00:02:54.070 --> 00:02:57.100
lines, you can kind of view
them as being similar-- is

00:02:57.100 --> 00:03:00.750
that magnetic forces always come
in dipoles, soon. while

00:03:00.750 --> 00:03:02.920
you could have electrostatic
forces that are monopoles.

00:03:02.920 --> 00:03:05.110
You could have just a positive
or a negative charge.

00:03:05.110 --> 00:03:07.100
So that's fine, you say,
Sal, that's nice.

00:03:07.100 --> 00:03:08.130
You drew these field lines.

00:03:08.130 --> 00:03:10.260
And you've probably seen it
before if you've ever dropped

00:03:10.260 --> 00:03:11.950
metal filings on top
of a magnet.

00:03:11.950 --> 00:03:13.070
They kind of arrange themselves

00:03:13.070 --> 00:03:13.930
along these field lines.

00:03:13.930 --> 00:03:15.440
But you might say, well,
that's kind of useful.

00:03:15.440 --> 00:03:21.520
But how do we determine the
magnitude of a magnetic field

00:03:21.520 --> 00:03:22.300
at any point?

00:03:22.300 --> 00:03:25.950
And this is where it
gets interesting.

00:03:25.950 --> 00:03:29.530
The magnitude of a magnetic
field is really determined, or

00:03:29.530 --> 00:03:33.340
it's really defined, in terms of
the effect that it has on a

00:03:33.340 --> 00:03:35.130
moving charge.

00:03:35.130 --> 00:03:36.580
So this is interesting.

00:03:36.580 --> 00:03:38.640
I've kind of been telling you
that we have this different

00:03:38.640 --> 00:03:42.110
force called magnetism that
is different than the

00:03:42.110 --> 00:03:43.610
electrostatic force.

00:03:43.610 --> 00:03:47.490
But we're defining magnetism in
terms of the effect that it

00:03:47.490 --> 00:03:48.500
has on a moving charge.

00:03:48.500 --> 00:03:49.510
And that's a bit of a clue.

00:03:49.510 --> 00:03:51.550
And we'll learn later, or
hopefully you'll learn later

00:03:51.550 --> 00:03:55.540
as you advance in physics,
that magnetic force or a

00:03:55.540 --> 00:04:00.200
magnetic field is nothing but an
electrostatic field moving

00:04:00.200 --> 00:04:02.040
at a very high speed.

00:04:02.040 --> 00:04:03.160
At a relativistic speed.

00:04:03.160 --> 00:04:06.160
Or you could almost view it as
they are the same thing, just

00:04:06.160 --> 00:04:07.730
from different frames
of reference.

00:04:07.730 --> 00:04:08.970
I don't want to confuse
you right now.

00:04:08.970 --> 00:04:12.730
But anyway, back to what I'll
call the basic physics.

00:04:12.730 --> 00:04:17.730
So if I had to find a magnetic
field as B-- so B is a vector

00:04:17.730 --> 00:04:23.610
and it's a magnetic field-- we
know that the force on a

00:04:23.610 --> 00:04:26.000
moving charge could be an
electron, a proton, or some

00:04:26.000 --> 00:04:29.190
other type of moving
charged particle.

00:04:29.190 --> 00:04:31.840
And actually, this is the basis
of how they-- you know,

00:04:31.840 --> 00:04:33.830
when you have supercolliders--
how they get the particles to

00:04:33.830 --> 00:04:36.030
go in circles, and how they
studied them by based on how

00:04:36.030 --> 00:04:38.110
they get deflected by
the magnetic field.

00:04:38.110 --> 00:04:42.820
But anyway, the force on a
charge is equal to the

00:04:42.820 --> 00:04:45.670
magnitude of the charge-- of
course, this could be positive

00:04:45.670 --> 00:04:49.090
or negative-- times, and this is
where it gets interesting,

00:04:49.090 --> 00:04:56.000
the velocity of the charge
cross the magnetic field.

00:04:56.000 --> 00:04:58.460
So you take the velocity of the
charge, you could either

00:04:58.460 --> 00:05:00.701
multiply it by the scalar first,
or you could take the

00:05:00.701 --> 00:05:02.220
cross product then multiply
it by the scalar.

00:05:02.220 --> 00:05:03.790
Doesn't matter because
it's just a number,

00:05:03.790 --> 00:05:04.990
this isn't a vector.

00:05:04.990 --> 00:05:07.220
But you essentially take the
cross product of the velocity

00:05:07.220 --> 00:05:09.400
and the magnetic field, multiply
that times the

00:05:09.400 --> 00:05:14.090
charge, and then you get the
force vector on that particle.

00:05:14.090 --> 00:05:15.930
Now there's something that
should immediately-- if you

00:05:15.930 --> 00:05:17.960
hopefully got a little bit of
intuition about what the cross

00:05:17.960 --> 00:05:19.240
product was-- there's something

00:05:19.240 --> 00:05:22.000
interesting going on here.

00:05:22.000 --> 00:05:25.760
The cross product cares about
the vectors that are

00:05:25.760 --> 00:05:27.750
perpendicular to each other.

00:05:27.750 --> 00:05:31.450
So for example, if the
velocity is exactly

00:05:31.450 --> 00:05:34.450
perpendicular to the magnetic
field, then we'll

00:05:34.450 --> 00:05:35.290
actually get a number.

00:05:35.290 --> 00:05:38.900
If they're parallel, then the
magnetic field has no impact

00:05:38.900 --> 00:05:40.180
on the charge.

00:05:40.180 --> 00:05:42.340
That's one interesting thing.

00:05:42.340 --> 00:05:44.680
And then the other interesting
thing is when you take the

00:05:44.680 --> 00:05:49.850
cross product of two vectors,
the result is perpendicular to

00:05:49.850 --> 00:05:51.630
both of these vectors.

00:05:51.630 --> 00:05:52.380
So that's interesting.

00:05:52.380 --> 00:05:56.040
A magnetic field, in order to
have an effect on a charge,

00:05:56.040 --> 00:05:59.080
has to be perpendicular
to its you velocity.

00:05:59.080 --> 00:06:01.830
And then the force on it is
going to be perpendicular to

00:06:01.830 --> 00:06:05.460
both the velocity of the charge
and the magnetic field.

00:06:05.460 --> 00:06:08.100
I know I'm confusing you at
this point, so let's play

00:06:08.100 --> 00:06:09.680
around with it and
do some problems.

00:06:09.680 --> 00:06:11.900
But before that, let's figure
out what the units of the

00:06:11.900 --> 00:06:13.700
magnetic field are.

00:06:13.700 --> 00:06:16.910
So we know that the cross
product is the same thing as--

00:06:16.910 --> 00:06:18.970
so let's say, what's the
magnitude of the force?

00:06:18.970 --> 00:06:24.790
The magnitude of the
force is equal to?

00:06:24.790 --> 00:06:26.580
Well, the magnitude of the
charge-- this is just a scalar

00:06:26.580 --> 00:06:31.380
quantity, so it's still just
the charge-- times the

00:06:31.380 --> 00:06:34.650
magnitude of the velocity times
the magnitude of the

00:06:34.650 --> 00:06:39.310
field times the sine of the
angle between them.

00:06:39.310 --> 00:06:41.230
This is the definition of a
cross product and then we

00:06:41.230 --> 00:06:44.050
could put-- if we wanted the
actual force vector, we can

00:06:44.050 --> 00:06:46.200
just multiply this times the
vector we get using the

00:06:46.200 --> 00:06:46.720
right-hand rule.

00:06:46.720 --> 00:06:48.080
We'll do that in a second.

00:06:48.080 --> 00:06:50.230
Anyway we're just focused
on units.

00:06:50.230 --> 00:06:53.350
Sine of theta has no units so
we can ignore it for this

00:06:53.350 --> 00:06:55.100
discussion.

00:06:55.100 --> 00:06:57.140
We're just trying to figure
out the units of

00:06:57.140 --> 00:06:59.370
the magnetic field.

00:06:59.370 --> 00:07:06.160
So force is newtons-- so we
could say newtons equals--

00:07:06.160 --> 00:07:12.350
charge is coulombs, velocity is
meters per second, and then

00:07:12.350 --> 00:07:17.910
this is times the-- I don't know
what we'll call this--

00:07:17.910 --> 00:07:21.040
the B units.

00:07:21.040 --> 00:07:22.662
We'll call it unit sub B.

00:07:22.662 --> 00:07:23.300
So let's see.

00:07:23.300 --> 00:07:25.780
If we divide both sides by
coulombs and meters per

00:07:25.780 --> 00:07:28.930
second, we get newtons
per coulomb.

00:07:28.930 --> 00:07:30.890
And then if we divide by meters
per second, that's the

00:07:30.890 --> 00:07:34.850
same thing as multiplying
by seconds per meter.

00:07:34.850 --> 00:07:39.800
Equals the magnetic
field units.

00:07:39.800 --> 00:07:45.380
So the magnetic field in SI
terms, is defined as newton

00:07:45.380 --> 00:07:48.080
seconds per coulomb meter.

00:07:48.080 --> 00:07:50.920
And that might seem a little
disjointed, and they've come

00:07:50.920 --> 00:07:51.970
up with a brilliant name.

00:07:51.970 --> 00:07:54.660
And it's named after a deserving
fellow, and that's

00:07:54.660 --> 00:07:55.910
Nikolai Tesla.

00:07:55.910 --> 00:08:01.400
And so the one newton second
per coulomb meter is

00:08:01.400 --> 00:08:07.210
equal to one tesla.

00:08:07.210 --> 00:08:10.150
And I'm actually running out of
time in this video, because

00:08:10.150 --> 00:08:11.650
I want to do a whole
problem here.

00:08:11.650 --> 00:08:15.390
But I just want you to sit and
think about it for a second.

00:08:15.390 --> 00:08:19.120
Even though in life we're used
to dealing with magnets as we

00:08:19.120 --> 00:08:22.200
have these magnets-- and they're
fundamentally maybe

00:08:22.200 --> 00:08:25.260
different than what at least we
imagine electricity to be--

00:08:25.260 --> 00:08:30.570
but the magnitude or actually
the units of magnetism is

00:08:30.570 --> 00:08:33.840
actually defined in terms of the
effect that it would have

00:08:33.840 --> 00:08:35.100
on a moving charge.

00:08:35.100 --> 00:08:38.840
And that's why the unit-- one
tesla, or a tesla-- is defined

00:08:38.840 --> 00:08:42.450
as a newton second
per coulomb.

00:08:42.450 --> 00:08:46.530
So the electrostatic charge
per coulomb meter.

00:08:46.530 --> 00:08:48.600
Well, I'll leave you
now in this video.

00:08:48.600 --> 00:08:49.810
Maybe you can sit
and ponder that.

00:08:49.810 --> 00:08:52.010
But it'll make a little bit
more sense when we do some

00:08:52.010 --> 00:08:53.940
actual problems with
some actual

00:08:53.940 --> 00:08:56.240
numbers in the next video.

00:08:56.240 --> 00:08:57.490
See