All right. We've seen how if you have an
electric current (that is, moving charges)
it creates a magnetic field, according to
the right-hand-rule
giving you circular lines of magnetic
field surrounding the wire
(which we'll use in just a minute). But it
turns out
(as they discovered in the early 1800s
it was Michael Faraday in 1831, in fact)
that a changing magnetic field
can also induce a current (an electric
current) in a wire.
We call this magnetic induction. And
this graphic here (this animated graphic)
shows us
that we have (let's say) a bar magnet
inside a loop
of wire and if that bar magnet leaves, a
current is induced in the wire.
Well, a that's maybe not so convincing
because it's just a a computer animation.
We can do it in real life here using
this
actual loop of wire. This is a,
you know, copper wire loop, many many
turns here connected to a simple
voltmeter.
Now we can do exactly the same thing as
is in the
animation up there, put a magnet inside
here and then
pull it out. And if you look carefully at
the tip
of the arrow on the voltmeter you see
that it moves. When the magnet goes in
you get a pulse.
You get a pulse the other direction when it goes out. Well that's not terribly impressive,
so we have a much more a much stronger
magnet here.
And if I take this loop and I pass it
in between the poles of the magnet (uh)
you'll see what happens.
Again, watch the tip of the arrow on the
voltmeter,
and you see you get a pulse of voltage in one direction when I go
in and then when I pull it out you get a pulse of voltage
in the other direction. And, indeed, there's
current flowing one way and then the other
way depending on whether
the flux is going in one direction or the
other.
Now I used that word "flux". What does that mean? Well,
there are a couple of ways to think about how this current is induced.
We already saw that if you have a
charged particle
and it's moving in a magnetic field it
feels a force.
Okay? Well imagine an electron in that loop of wire.
As its going
past the the magnetic field lines here
it feels a force in a certain direction
and if you work out for every electron
in the loop
(the force that it feels) there's a net
current in one direction or the other
depending on which way
the the charge is moving. So that's one way to think about it, just in terms of the
magnetic force we already know about. But we can also describe it
in terms of magnetic flux. And how does
that work?
Uh, Lenz's Law, which
came just a few years after Faraday's
discovery of this effect,
says that the current that's induced in
a loop of wire
(uh) flows in a direction which tends to
oppose the change
in magnetic flux through the loop. So
first we have to understand what is
magnetic flux.
Uh, if you have a magnetic field, which we
call B,
and (uh) suppose, you know, there's magnetic field lines all over this loop,
if we take the magnetic field, multiply it
by the area, that gives us (the magnetic
field)
the magnetic flux. You should think of the
magnetic flux as
basically the total number of magnetic
field lines (uh
times the) times the area here. Or you
could think of it as just the number
field lines, if you want. Now this is a
vector quantity.
It's pointing to the right here because
we have (this magnet going)
the magnetic field lines inside the
magnet (is) going from south to north and
remember they curve around
and then they go back in the South end. Uh,
as the magnet leaves the loop then this
a magnetic flux goes from pointing in
the right hand direction to
well a smaller (uh, uh)
vector, still pointing to the right. I say on the slide it goes from right to left, but it
doesn't quite go all the way
to the left because we still have a weak
magnetic field going
(into, from the) from out here into the
South Pole of the magnet.
But if you have the magnetic flux
changing from positive to negative,
you'll get
an induced current in the loop. We can
figure out that direction
from Lenz's law by considering
what is the change in flux and what
current would you need to oppose that
change.
So let's use our right-hand-rule to do that.
In this diagram
(the uh) the loop is such that's its going into the screen here.
So suppose we have a current which is
going
up, what magnetic field will that produce?
Well,
we use our right-hand-rule where we grasp the wire, thumb going in the direction of
the current,
and then our fingers wrap in the direction above the magnetic field lines.
And, indeed, you see that
your fingertips so than pointing in that
direction (out
of, or) to the right, in this in this
drawing.
And so (uh) by having a current
creating such a magnetic field, that
tends to oppose the change that we made by
removing the magnet, okay? So, again,
magnetic flux is just the magnetic field
times the area. If you have a uniform
magnetic field like the one shown here,
pointing to the right,
all the arrows point along the magnetic
field lines to the right
(and it) and the magnetic field is the same everywhere
on the loop, then if the loop is oriented
perpendicularly to the field
the flux is just given by B, the magnetic
field
strength, times the area.
Now imagine we take the loop and we turn it flat
so that none of the magnetic field lines
are going through it. In that case, even
though you're still
in a region where there's a magnetic
field (a uniform magnetic field),
none of the field lines go through the loop
and, hence, the magnetic flux is equal to 0.
So just by taking this loop and turning
it sideways
we've gone from having some flux to
having zero flux.
And the current that's induced in the loop
is proportional to the time rate of
change
of the magnetic flux through the
loop. Now this is the
physics on which a very common and very useful device is built, the electric
generator.
If you have any source of mechanical energy which can turn a crank,
whether it's (uh), you know, your hand turning the crank, a wind turbine, water,
even. you know, steam turbine from, you know, where the steam is heated from
a nuclear power plant (anything that
gives you mechanical,
uh, force turning a shaft) can turn a loop
of wire
and if you turn it in a big magnetic
field created by permanent magnets
then you will get an electric current
induced in that loop. And that's sort of
indicated, schematically, here with this
big (uh)
C-shaped magnet here and you turn the
crank
and this loop turns. As you turn the loop,
the flux through that loop
is oscillating up and down sinusoidally
and hence the current that's induced (and goes through the the light bulb here) is a
sinusoidal
current. That's what we call alternating
current and that's one of the reasons
that we have alternating current
as (uh) the dominant (uh) electrical power
source
all over the world is that it's based on
generators whose
shaft is rotating sixty times a second
(or fifty times a second) depending on
where you are in the world
