Overview of cell signaling

WEBVTT
Kind: captions
Language: en

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- [Voiceover] What I
wanna do in this video

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is give ourselves a quick
overview of the different ways

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that cells can communicate
with each other.

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And maybe the most basic one,

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is just through direct contact

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and this can happen
several different ways.

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One way could be,

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you just have neighboring cells

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so this is one cell right over here,

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and this is the neighboring
cell right over here.

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And they actually might have
gaps in their membranes.

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If these are plant cells

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we would call these gaps, gap junctions.

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I just drew two of them
and this is obviously

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just a two-dimensional slice.

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So we're not fully appreciating

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the three-dimensional structure,

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but the basic idea is that
maybe the cell on the left

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starts producing some molecules,

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especially some small molecules

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that are able to go through
these gap junctions.

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And when they're able to go
through the gap junctions,

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maybe they latch on to some
proteins in the second cell

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that start maybe activating
them in a certain way,

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or inhibit them in a certain way,

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or trigger some type of reaction.

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And so then you have a
response in the second cell.

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So this would be a form of communication.

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Something happened in this first cell

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to produce these molecules.

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Those molecules were able
to get into the second cell,

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and trigger a response.

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And as I mentioned, if
these are animal cells,

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we would call these gaps,

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we'd call them gap junctions.

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So that right over there,

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that is a gap junction.

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And we covered this in other videos.

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And if we're talking about plant cells

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we can have very similar things happening,

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but we wouldn't call them gap junctions.

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These would be gaps,

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not even tunnels through the membrane,

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it would also be through the cell walls.

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If we were talking about plants,

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they would be plasmodesmata.

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And we'd talk about these more

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in The Structure of Cell videos.

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But there is other ways
that you could communicate

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via direct contact.

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You could imagine maybe some cells

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that are floating around
in the blood stream.

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Maybe this is one cell over here,

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maybe this is another cell over here.

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And they have complementary
surface proteins.

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Surface proteins that are
able to bind to each other.

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So maybe this one has a surface protein

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that looks like this.

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I'm obviously exaggerating its shape,

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the protein wouldn't look exactly like

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this inverted triangle.

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But this one has a
surface protein like this,

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and I'm also exaggerating
it's size relative to a cell,

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just so we can appreciate

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how they could maybe lock together.

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So this one has a surface
protein like that.

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And when they bind to each other

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it might change the proteins in some way,

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and then trigger a reaction
in each of these cells.

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That the communication then continues.

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If this protein changes a little bit,

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it might activate something.

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It might activate the
release of some molecules,

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it might activate some other proteins,

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it might catalyze some type of reaction.

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We've seen this in multiple other videos,

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all sorts of crazy biological reactions

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can happen inside of cells.

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But it might illicit a,

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it could illicit a response.

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And actually it could even
illicit a response in both cells,

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some type of response.

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They know that they are
latched-on to someone else.

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Now direct contact you could imagine,

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is not the only way that you
could have cell-cell signaling.

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You could actually have
cells start to signal

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over a little bit of a distance,

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by releasing molecules into
the extracellular space

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and eventually even into the blood stream.

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So, for example,

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let me draw a cell right over here,

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and maybe it's able to
produce some molecules.

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And these molecules either,

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they might be lipid soluble
and maybe make their way

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through the cellular
membrane on their own.

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Or, maybe they are packed in nice vesicles

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that allow them to traverse the membrane.

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So when you get actually,

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so the membrane of the vesicle

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merges with the membrane of the cell.

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And then it allows

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these things to get out.

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And so you could imagine,

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if another cell has the
right receptors for these,

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that would signal some type of a response

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or it will form some
form of communication.

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So let's say that I have,

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actually let me draw a couple of cells.

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So let's say I have this cell over here,

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and then I have this cell over here.

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And let's say that this
cell has the right receptor,

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and this cell doesn't.

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It could have other receptors,

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maybe it has receptors like that

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but it's not the right receptor.

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And so these molecules that
were released by this first cell

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could bind not on this character,

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not on this surface protein,

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but it could bind on this character.

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So it could bind on this character

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and when it does so,

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this protein that's on
the cellular membrane,

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it might change its shape,

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it might do all sorts of things.

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But that signal can be then taken somehow,

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it can continue on into
the cell and once again,

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you might illicit some type of response.

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And we'll go into more
detail in future videos

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on exactly how that happens,

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or what these responses actually might be.

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Now, if this is over a short distance,

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if this is a short distance,

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short distance,

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we would call this paracrine.

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This would be part of
the paracrine system,

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or we would call this
paracrine communication.

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Let me write that down,

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paracrine system,

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or paracrine communication,

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or paracrine signaling,

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and we would call these paracrine factors.

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But if it was happening
over long distances,

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say maybe these molecules

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they enter into the blood stream,

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so they make their way
into the blood stream

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right over here.

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So let me depict somehow that
this is the blood stream.

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So this is the blood stream,

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and they're able to go
through the blood stream

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over longer distances to other molecules.

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So maybe this one has the right receptors

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for those molecules.

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Then we'd call this the endocrine system,

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or this is endocrine signaling.

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So long distances,

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we would call this the endocrine system,

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or endocrine signaling.

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And we're talking about
the endocrine system

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and endocrine signaling,

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these molecules which could just be,

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there could be all sorts of
different types of molecules.

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They could be steroids,

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they could be proteins of some kind.

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In this case, we would call them hormones.

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And you've probably heard the word before

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and we will do a whole
series of videos on hormones.

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But these molecules
actually could even affect

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the cell that produced them.

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For example, the cell that produced it

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might have the right receptor.

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And so, if it's able to signal,

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if it's able to trigger
a reaction in itself,

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so if these things are able to
trigger a reaction in itself,

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we would call that an autocrine process.

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It is acting on itself.

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And just so you're familiar
with some of the terminology,

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these proteins on the surface,

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and this would be the case
especially if you have

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non-lipid soluble types
of signaling factors,

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or molecules right over here.

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These proteins, actually even
if they're on the surface

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or even if they're within the cell,

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we would call them receptors.

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So that right over there,

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that is a receptor.

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And the molecules themselves,

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these things that bind on to the receptor,

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we call them the ligand.

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In general, it's the
general term for something

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that binds on to a receptor.

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And so at that point where
you bind on to a receptor,

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whether you're talking
about the paracrine process

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or endocrine,

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actually endo, I left a C out here,

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endocrine signaling,

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this process where it latches on,

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we would call that a signal perception.

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And then when this protein
somehow changes its shape,

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or starts catalyzing a reaction,

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or inhibiting a reaction,

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we would call this the
signal transduction.

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It's bringing the signal into the cell.

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And then you have,

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you have your actual cellular response.

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So hopefully you appreciate that

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as just a bit of an overview

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of how cells can signal with each other.

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And in future videos we'll go
into a little bit more detail.

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Especially the endocrine system,

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and our understanding of hormones.


Walk through of STEM content on KA

WEBVTT
Kind: captions
Language: en

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- [Voiceover] There is a lot
of content on Khan Academy,

00:00:02.718 --> 00:00:04.084
especially in math and science,

00:00:04.084 --> 00:00:07.684
and we're continuing to add
more and more content everyday

00:00:07.684 --> 00:00:09.517
in math and science and in other areas

00:00:09.517 --> 00:00:12.117
like history and art
history and wherever else.

00:00:12.117 --> 00:00:15.484
But I want to do in this
video is make sense of

00:00:15.484 --> 00:00:18.484
some potential progressions,
especially in math and science.

00:00:18.484 --> 00:00:20.284
And see how all of these
different topics relate

00:00:20.284 --> 00:00:23.217
to each other in ways that
we can use Khan Academy.

00:00:23.217 --> 00:00:27.818
In blue here, I have a
proposed math progression.

00:00:27.818 --> 00:00:30.151
So we have a mission on Khan Academy,

00:00:30.151 --> 00:00:33.184
it's called early math, it's
also called the K-2 mission.

00:00:33.184 --> 00:00:34.750
When I talk about missions, this is where

00:00:34.750 --> 00:00:36.784
you take a diagnostic and
based on that it starts

00:00:36.784 --> 00:00:39.384
recommending things and then
there are master challenges,

00:00:39.384 --> 00:00:41.817
all of these game
mechanics, and you can work

00:00:41.817 --> 00:00:43.051
at your own time and pace.

00:00:43.051 --> 00:00:45.684
You can also access these,
what we call in library mode,

00:00:45.684 --> 00:00:47.151
where you can just pick and choose

00:00:47.151 --> 00:00:48.751
which exercises you want to practice,

00:00:48.751 --> 00:00:52.251
or which videos or articles
you want to take a look at.

00:00:52.251 --> 00:00:56.484
What I recommend a student
do, if they haven't already,

00:00:56.484 --> 00:00:59.551
master the early learning mission,

00:00:59.551 --> 00:01:01.051
finish that all the way
to one hundred percent,

00:01:01.051 --> 00:01:02.984
then do third grade,
fourth grade, fifth grade,

00:01:02.984 --> 00:01:05.417
sixth grade and then seventh grade.

00:01:05.417 --> 00:01:06.984
Once you start getting into the

00:01:06.984 --> 00:01:08.585
sixth and seventh grade range,

00:01:08.585 --> 00:01:11.318
you're starting to do a
little bit of pre-algebra.

00:01:11.318 --> 00:01:13.918
And as you see, once you
get past seventh grade,

00:01:13.918 --> 00:01:16.984
a whole new world starts to open up.

00:01:16.984 --> 00:01:19.651
So once you get past seventh
grade, you start getting into

00:01:19.651 --> 00:01:24.517
some real algebra and my map here

00:01:24.517 --> 00:01:26.518
starts to get a little more complex.

00:01:26.518 --> 00:01:28.517
But what you see going on here is,

00:01:28.517 --> 00:01:30.017
you have an algebra basics mission,

00:01:30.017 --> 00:01:33.051
and the idea of that, that's
actually a bit of a subset

00:01:33.051 --> 00:01:34.650
of what you would see in the eighth grade

00:01:34.650 --> 00:01:36.450
algebra one, algebra two missions,

00:01:36.450 --> 00:01:38.218
although there's a few
extra things relative

00:01:38.218 --> 00:01:40.217
to the eighth grade mission.

00:01:40.217 --> 00:01:43.917
But it's the very core of algebra,

00:01:43.917 --> 00:01:46.418
and you can see that if you
were to finish that mission

00:01:46.418 --> 00:01:49.217
all sorts of extra things open up.

00:01:49.217 --> 00:01:51.085
Now if you want to know your algebra

00:01:51.085 --> 00:01:53.617
more comprehensibly, and
I encourage you to do so,

00:01:53.617 --> 00:01:55.884
you should complete the
eighth grade mission,

00:01:55.884 --> 00:01:58.984
the algebra one mission and
the algebra two missions.

00:01:58.984 --> 00:02:00.351
And what you'll see is if you finish

00:02:00.351 --> 00:02:02.051
the algebra basics mission,
the eighth grade mission

00:02:02.051 --> 00:02:05.051
isn't that much incremental
work or vice versa.

00:02:05.051 --> 00:02:07.250
And if you finish these
and the algebra one mission

00:02:07.250 --> 00:02:08.884
isn't that much incremental work,

00:02:08.884 --> 00:02:10.984
it gives you credit
for where they overlap.

00:02:10.984 --> 00:02:13.051
And if you finish these
three, the algebra two mission

00:02:13.051 --> 00:02:15.184
isn't that much incremental work.

00:02:15.184 --> 00:02:16.784
But if you were to do this collection,

00:02:16.784 --> 00:02:20.017
you have a really solid
foundation for algebra

00:02:20.017 --> 00:02:24.767
and all sorts of things start
to become available for you.

00:02:24.767 --> 00:02:26.584
If you're going to do the
algebra basics mission,

00:02:26.584 --> 00:02:29.016
you are fairly well
equipped to start thinking

00:02:29.016 --> 00:02:31.752
about things like finance
and capital markets,

00:02:31.752 --> 00:02:35.417
microeconomics, macroeconomics.

00:02:35.417 --> 00:02:37.218
If you do the algebra basics mission

00:02:37.218 --> 00:02:39.151
you're also ready for biology,

00:02:39.151 --> 00:02:41.050
a lot of biology doesn't
have mathematics in it,

00:02:41.050 --> 00:02:42.917
but there is some algebra once

00:02:42.917 --> 00:02:44.584
you start getting in to biology.

00:02:44.584 --> 00:02:46.253
In fact there some
probability and statistics,

00:02:46.253 --> 00:02:48.417
some basics probability and statistics

00:02:48.417 --> 00:02:50.718
once you start getting
into things like genetics.

00:02:50.718 --> 00:02:53.584
So I encourage you to have that
nice foundation in algebra.

00:02:53.584 --> 00:02:56.951
Chemistry too, there
isn't math throughout it,

00:02:56.951 --> 00:02:58.384
there isn't algebra throughout it,

00:02:58.384 --> 00:03:00.684
there actually is math
throughout chemistry,

00:03:00.684 --> 00:03:02.484
but the algebra will help you go into,

00:03:02.484 --> 00:03:05.717
you will start seeing
some types of problems

00:03:05.717 --> 00:03:06.819
where you will have to solve

00:03:06.819 --> 00:03:08.251
a quadratic or things like that.

00:03:08.251 --> 00:03:11.417
So it is useful to have a
solid foundation in algebra.

00:03:11.417 --> 00:03:13.283
If you want to go into physics,

00:03:13.283 --> 00:03:14.717
this is where the algebra,

00:03:14.717 --> 00:03:18.317
the physics on Khan Academy is
currently non-calculus based,

00:03:18.317 --> 00:03:20.317
we're going to add calculus based soon,

00:03:20.317 --> 00:03:21.851
but in order to engage with it,

00:03:21.851 --> 00:03:24.718
you have to have a very
solid foundation in algebra,

00:03:24.718 --> 00:03:26.217
that's where this arrow comes from,

00:03:26.217 --> 00:03:28.384
and you need to know the
basics of trigonometry,

00:03:28.384 --> 00:03:29.784
that's why I drew this dotted arrow.

00:03:29.784 --> 00:03:34.217
You should know what a sine,
cosine, tangent of angles are,

00:03:34.217 --> 00:03:36.918
and the kind of right triangle definitions

00:03:36.918 --> 00:03:40.850
or the unit circle definitions
of those trig functions,

00:03:40.850 --> 00:03:43.152
and that's just the very
basics of trigonometry.

00:03:43.152 --> 00:03:44.884
But once you know that,
the basics of algebra,

00:03:44.884 --> 00:03:46.517
the basics of trigonometry,

00:03:46.517 --> 00:03:48.450
you're ready to engage in physics.

00:03:48.450 --> 00:03:49.784
And related to physics of course,

00:03:49.784 --> 00:03:53.158
and really based on physics,
is cosmology and astronomy.

00:03:53.158 --> 00:03:55.017
Once again if you have
the basics of algebra,

00:03:55.017 --> 00:03:59.551
you're really ready to start
engaging on that front.

00:03:59.551 --> 00:04:02.284
What about math, well
you can just keep going.

00:04:02.284 --> 00:04:03.618
If you have the basics of algebra,

00:04:03.618 --> 00:04:05.451
you can start going into
probability and statistics

00:04:05.451 --> 00:04:07.018
which is also super foundational.

00:04:07.018 --> 00:04:08.984
If you were to go to
graduate school one day

00:04:08.984 --> 00:04:10.984
or do research in almost anything,

00:04:10.984 --> 00:04:13.518
probability and statistics is core.

00:04:13.518 --> 00:04:16.651
Frankly, any profession that you go into

00:04:16.651 --> 00:04:19.764
there will be a lot of
probability and statistics.

00:04:19.764 --> 00:04:24.217
We can keep going, geometry is neat area,

00:04:24.217 --> 00:04:28.295
is a neat subject because
not only will you be

00:04:28.295 --> 00:04:31.451
studying things we traditionally
associate with geometry,

00:04:31.451 --> 00:04:35.550
but it's really the first
domain that you will see where

00:04:35.550 --> 00:04:40.017
you're going to think about
proofing things rigorously.

00:04:40.017 --> 00:04:43.188
So once you get this good
foundation in algebra and geometry

00:04:43.188 --> 00:04:46.451
you're ready to really
dive into trigonometry,

00:04:46.451 --> 00:04:48.051
and once you have all of that built out

00:04:48.051 --> 00:04:49.950
you can go to calculus.

00:04:49.950 --> 00:04:51.684
Which will you find fascinating,

00:04:51.684 --> 00:04:54.584
which opens up the world
up multi variable calculus,

00:04:54.584 --> 00:04:57.151
differential equations and linear algebra

00:04:57.151 --> 00:05:00.650
is typically taken when you're
in college after calculus.

00:05:00.650 --> 00:05:02.918
But really to engage in linear algebra

00:05:02.918 --> 00:05:05.518
you need a solid foundation in algebra

00:05:05.518 --> 00:05:09.351
and a bit of foundation in trigonometry.

00:05:09.351 --> 00:05:11.751
So I encourage you to
go on that progression.

00:05:11.751 --> 00:05:14.318
Now we also see things like SAT,

00:05:14.318 --> 00:05:16.650
of course the standardized test,

00:05:16.650 --> 00:05:19.284
that's a big part of college admissions.

00:05:19.284 --> 00:05:22.251
And I encourage you to
engage on the test prep

00:05:22.251 --> 00:05:24.350
for the SAT on Khan Academy that

00:05:24.350 --> 00:05:26.652
we do in conjunction
with the college board.

00:05:26.652 --> 00:05:30.250
Not just because it will
hopefully improve your SAT score,

00:05:30.250 --> 00:05:32.617
but the SAT is a measure
of college readiness.

00:05:32.617 --> 00:05:35.484
So the better that you're
able to do on this,

00:05:35.484 --> 00:05:38.817
this is a solid indicator
of your college readiness.

00:05:38.817 --> 00:05:41.584
You can really start to
engage on that SAT practice

00:05:41.584 --> 00:05:44.451
as soon as you have a solid
foundation of the algebra.

00:05:44.451 --> 00:05:47.217
So as soon as you have the
algebra basics mission done,

00:05:47.217 --> 00:05:49.417
I encourage you to go
into the SAT mission.

00:05:49.417 --> 00:05:52.817
To really engage in
everything on the SAT mission,

00:05:52.817 --> 00:05:57.084
especially on the math
side or the SAT prep,

00:05:57.084 --> 00:05:59.551
I encourage you to also
get through the algebra two

00:05:59.551 --> 00:06:02.407
because there are going
to be some functions

00:06:02.407 --> 00:06:05.250
and the other pieces here
that I haven't talked about.

00:06:05.250 --> 00:06:07.686
Here are the programming,
and you can start programming

00:06:07.686 --> 00:06:10.618
on Khan Academy for those
of you who haven't seen it

00:06:10.618 --> 00:06:12.884
it's a lot of fun, you
get to work on projects

00:06:12.884 --> 00:06:14.117
and share it with your friends,

00:06:14.117 --> 00:06:16.218
and there's even a peer review mechanism.

00:06:16.218 --> 00:06:18.051
You can start engaging with
that at a fairly early level.

00:06:18.051 --> 00:06:20.684
Once you have some of
your core arithmetic done,

00:06:20.684 --> 00:06:23.351
but obviously the more math
you have behind you the better.

00:06:23.351 --> 00:06:27.985
But then once you get through
some of these core subjects

00:06:27.985 --> 00:06:31.251
that we've been talking about,
especially basic algebra,

00:06:31.251 --> 00:06:33.617
the very basics of trigonometry then

00:06:33.617 --> 00:06:35.684
you can start going into
advanced JavaScript.

00:06:35.684 --> 00:06:37.351
And algorithms.

00:06:37.351 --> 00:06:39.651
Advanced JavaScript
you'll especially enjoy

00:06:39.651 --> 00:06:42.251
because here you can do
simulations of nature,

00:06:42.251 --> 00:06:44.351
simulations of some of
the things you will learn

00:06:44.351 --> 00:06:45.884
in these science topics.

00:06:45.884 --> 00:06:49.250
Or you can really start
to make video games.

00:06:49.250 --> 00:06:51.451
Hopefully this gives you a
good sense of what's available,

00:06:51.451 --> 00:06:54.018
especially on the math,
science side of Khan Academy.

00:06:54.018 --> 00:06:56.117
And in a way that you
can progress through it.

00:06:56.117 --> 00:06:58.934
And if you really, all of these things,

00:06:58.934 --> 00:07:00.468
the things in blue from early math

00:07:00.468 --> 00:07:03.817
all the way through calculus,
there are missions for.

00:07:04.957 --> 00:07:06.984
So all of this stuff right over here,

00:07:06.984 --> 00:07:08.584
there's these missions for which are these

00:07:08.584 --> 00:07:11.084
interactive, give you as
many exercises as you need,

00:07:11.084 --> 00:07:12.684
all of these game mechanics,

00:07:12.684 --> 00:07:16.050
SAT also has an interactive tool for,

00:07:16.050 --> 00:07:18.717
but the things where we
don't have missions yet,

00:07:18.717 --> 00:07:21.251
I encourage you to go through the videos,

00:07:21.251 --> 00:07:23.550
go one by one, if I'm going to go work,

00:07:23.550 --> 00:07:26.084
or whoever in the video who
is doing a work example,

00:07:26.084 --> 00:07:28.517
try to pause the video and see
if you can do it on your own.

00:07:28.517 --> 00:07:32.218
If you see me do it, look at
the video then stop the video

00:07:32.218 --> 00:07:34.152
and try to do that work over again,

00:07:34.152 --> 00:07:36.884
do the exercises there, I
think you'll be surprised

00:07:36.884 --> 00:07:38.784
by how much you can actually learn.

00:07:38.784 --> 00:07:40.317
We get a lot of testimonials every day,

00:07:40.317 --> 00:07:42.118
from people all walks of life

00:07:42.118 --> 00:07:44.017
who thought that they
weren't good at math,

00:07:44.017 --> 00:07:45.717
or who thought they
weren't good at science,

00:07:45.717 --> 00:07:47.584
but when they worked step by step,

00:07:47.584 --> 00:07:48.951
they build their foundations,

00:07:48.951 --> 00:07:51.184
they go back to any gaps
that they might have,

00:07:51.184 --> 00:07:53.550
over and over again people are surprised

00:07:53.550 --> 00:07:56.117
by how much they are
actually able to progress.

00:07:56.117 --> 00:07:58.218
And just as a reminder, this
isn't all the content on

00:07:58.218 --> 00:08:02.051
Khan Academy, we have some
great content on the humanities,

00:08:02.051 --> 00:08:04.018
history, art history, we're adding

00:08:04.018 --> 00:08:05.851
a whole set of partner content,

00:08:05.851 --> 00:08:07.817
and we're working on a
whole bunch of things

00:08:07.817 --> 00:08:10.000
as we speak, so enjoy.


Faraday's Law for generating electricity

WEBVTT
Kind: captions
Language: en

00:00:00.455 --> 00:00:01.126
- [Voiceover] We're already looked at

00:00:01.126 --> 00:00:02.588
Faraday's law in some detail.

00:00:02.588 --> 00:00:05.671
It showed us that if we have some

00:00:05.671 --> 00:00:09.554
loop of conductor and we have a change

00:00:09.554 --> 00:00:12.667
in magnetic flux over
time through the surface

00:00:12.667 --> 00:00:14.598
defined by that loop, it's going to induce

00:00:14.598 --> 00:00:17.198
an EMF through that loop which will cause

00:00:17.198 --> 00:00:22.198
a current to start to
circulate through that loop

00:00:22.399 --> 00:00:23.732
and that current, of
course, will be dependent

00:00:23.732 --> 00:00:26.597
on the actual resistance of the conductor.

00:00:26.597 --> 00:00:28.242
And there's many ways
that we've already seen

00:00:28.242 --> 00:00:30.477
of having a change in magnetic flux.

00:00:30.477 --> 00:00:33.444
One, you can have a change
in the magnetic field.

00:00:33.444 --> 00:00:35.435
It could be a change in its magnitude

00:00:35.435 --> 00:00:37.085
and, or it's orientation.

00:00:37.085 --> 00:00:39.198
You could have a change in the shape

00:00:39.198 --> 00:00:41.540
of the actual loop of conductor.

00:00:41.540 --> 00:00:43.754
If its area increases or decreases,

00:00:43.754 --> 00:00:45.197
that will change the flux.

00:00:45.197 --> 00:00:46.904
Remember, the flux is just your,

00:00:46.904 --> 00:00:49.098
the component of the magnetic field

00:00:49.098 --> 00:00:51.759
that is perpendicular to the surface.

00:00:51.759 --> 00:00:53.263
If you took the average of that times

00:00:53.263 --> 00:00:55.376
the area of the surface.

00:00:55.376 --> 00:00:56.303
And then the other way that we're going

00:00:56.303 --> 00:01:01.303
to study in this video is
inducing an electromotive force

00:01:03.026 --> 00:01:06.196
by changing it, not the shape of the loop

00:01:06.196 --> 00:01:08.085
and not the magnetic field but by changing

00:01:08.085 --> 00:01:10.077
the orientation of the loop.

00:01:10.077 --> 00:01:13.795
And in particular, we're
going to have the loop rotate.

00:01:13.795 --> 00:01:15.583
So let's think about this.
So I have this loop here.

00:01:15.583 --> 00:01:18.306
It's connected to this axle
and I'm going to rotate it

00:01:18.306 --> 00:01:22.207
in a, I'm going to rotate
it in a clockwise direction

00:01:22.207 --> 00:01:24.137
through this constant magnetic field.

00:01:24.137 --> 00:01:25.356
You can see it's constant.

00:01:25.356 --> 00:01:27.631
All of the magnetic field vectors

00:01:27.631 --> 00:01:29.911
I've just sampled'em at
different points in the field.

00:01:29.911 --> 00:01:31.955
They're all pointing straight
up and I've drawn them

00:01:31.955 --> 00:01:34.089
so that they all have the same magnitude.

00:01:34.089 --> 00:01:36.980
Now we'd appreciate is as we rotate this,

00:01:36.980 --> 00:01:39.703
the angle between the magnetic field

00:01:39.703 --> 00:01:42.628
and the surface is changing
and right from this point,

00:01:42.628 --> 00:01:44.822
as we rotated this clockwise direction,

00:01:44.822 --> 00:01:46.834
the component of the magnetic field

00:01:46.834 --> 00:01:51.834
that is perpendicular to the
surface is going to increase.

00:01:51.852 --> 00:01:53.071
Now what am I talking about?

00:01:53.071 --> 00:01:54.416
Well, let's look at it
from this point of view.

00:01:54.416 --> 00:01:55.920
Let's look at it from the point of view

00:01:55.920 --> 00:01:59.821
of the actual loop of wire,
so from this point of view

00:01:59.821 --> 00:02:01.873
the magnetic field is at some angle.

00:02:01.873 --> 00:02:05.306
I can draw that angle here
so, you know, whatever angle,

00:02:05.306 --> 00:02:08.029
it's a little hard to see,
whatever angle this is,

00:02:08.029 --> 00:02:09.898
we could say that is that angle here

00:02:09.898 --> 00:02:12.640
and as we rotate the
entire loop, it's attached

00:02:12.640 --> 00:02:16.095
to some type of an axle here,
in a clockwise direction.

00:02:16.095 --> 00:02:18.289
What is going to happen to this angle?

00:02:18.289 --> 00:02:20.902
Well, after let's say delta
T, let's say we're just

00:02:20.902 --> 00:02:25.782
rotating it a constant
rate, we're going to have

00:02:25.782 --> 00:02:29.297
the magnetic, so after
we've rotated a little bit,

00:02:29.297 --> 00:02:31.280
the magnetic field of vector is going

00:02:31.280 --> 00:02:32.946
to look something like that.

00:02:32.946 --> 00:02:35.510
So it's the component
that is perpendicular

00:02:35.510 --> 00:02:37.916
to the surface was what
we care about for flux,

00:02:37.916 --> 00:02:41.085
it's going to go from being
like this, it's gonna go

00:02:41.085 --> 00:02:45.007
from being like that to going to being,

00:02:45.007 --> 00:02:48.765
to being like this, to being like this.

00:02:48.765 --> 00:02:51.894
So at least for this
point of the rotation,

00:02:51.894 --> 00:02:53.377
for this point of the rotation till we get

00:02:53.377 --> 00:02:55.502
to the flat, until we
get to the flat point,

00:02:55.502 --> 00:02:59.017
until we have our loop
being completely flat,

00:02:59.017 --> 00:03:02.653
the component of our magnetic field

00:03:02.653 --> 00:03:05.356
that is perpendicular is going to increase

00:03:05.356 --> 00:03:07.205
which is going to have,
so we're going to have

00:03:07.205 --> 00:03:10.296
an increase in flux over that time.

00:03:10.296 --> 00:03:12.490
So if we have an increase
in flux over that time

00:03:12.490 --> 00:03:15.456
as we rotate up, at least
until we get to the flat point,

00:03:15.456 --> 00:03:16.492
what is going to happen?

00:03:16.492 --> 00:03:17.955
Well, we're going to induce a current

00:03:17.955 --> 00:03:19.030
and then we just have to think about what

00:03:19.030 --> 00:03:20.812
is the orientation of the current?

00:03:20.812 --> 00:03:22.526
So we want to have a current that

00:03:22.526 --> 00:03:23.806
will induce a magnetic field that will

00:03:23.806 --> 00:03:26.651
go against the change
in flux so the current

00:03:26.651 --> 00:03:29.394
should induce a magnetic field that is,

00:03:29.394 --> 00:03:31.771
if our flux, at least for
that part of the rotation

00:03:31.771 --> 00:03:35.733
is increasing in the upwards direction,

00:03:35.733 --> 00:03:39.097
if we're from the point
of view of this loop,

00:03:39.097 --> 00:03:41.635
then we need to create a magnetic field

00:03:41.635 --> 00:03:43.728
that is acting against that.

00:03:43.728 --> 00:03:46.471
So magnetic field that
is acting against that

00:03:46.471 --> 00:03:48.483
or we need to, we're
ready to induce a current

00:03:48.483 --> 00:03:50.026
that induces a magnetic field that acts

00:03:50.026 --> 00:03:52.059
against that change in flux.

00:03:52.059 --> 00:03:54.313
So, how do I, what type of current

00:03:54.313 --> 00:03:56.101
would induce a magnetic field like that?

00:03:56.101 --> 00:03:57.535
So I'll just use the
right-hand rule, my fingers

00:03:57.535 --> 00:03:59.383
would go in the direction of these,

00:03:59.383 --> 00:04:02.553
of the magnetic field, so my fingers

00:04:02.553 --> 00:04:04.260
and I have to use my right hand,

00:04:04.260 --> 00:04:06.555
so my fingers are gonna
go in that direction,

00:04:06.555 --> 00:04:08.404
so my right hand, my thumb,

00:04:08.404 --> 00:04:12.326
my thumb would go in this direction.

00:04:12.326 --> 00:04:14.032
So that is going to be the direction

00:04:14.032 --> 00:04:16.145
of the current that is induced.

00:04:16.145 --> 00:04:17.933
So the whole point of me showing you this,

00:04:17.933 --> 00:04:19.518
is that there's multiple ways to have

00:04:19.518 --> 00:04:22.342
a change in magnetic flux and there's

00:04:22.342 --> 00:04:26.019
multiple ways to induce a current.

00:04:26.019 --> 00:04:28.173
And this one is particularly interesting

00:04:28.173 --> 00:04:30.977
because it lets you or we
can start to think about,

00:04:30.977 --> 00:04:35.193
wow, I could turn, I could
turn a mechanical rotation

00:04:35.193 --> 00:04:39.500
into an induced current and
this is, this basic principle

00:04:39.500 --> 00:04:41.898
although they wouldn't use
such a simple loop like this,

00:04:41.898 --> 00:04:44.560
is exactly how electric generators work.

00:04:44.560 --> 00:04:45.534
They're actually, in some ways,

00:04:45.534 --> 00:04:46.814
the reverse of an electric motor.

00:04:46.814 --> 00:04:48.847
An electric motor has a current

00:04:48.847 --> 00:04:50.452
that causes something to rotate.

00:04:50.452 --> 00:04:52.077
Here, we're having something rotate

00:04:52.077 --> 00:04:54.576
causing a current to
form and that's actually

00:04:54.576 --> 00:04:56.647
what we have happening when you look

00:04:56.647 --> 00:04:58.660
at something like windmills or

00:04:58.660 --> 00:05:00.285
when you look at hydroelectric generators.

00:05:00.285 --> 00:05:02.255
Right over here, this windmill, the wind

00:05:02.255 --> 00:05:05.164
is going to cause these
blades to turn around

00:05:05.164 --> 00:05:07.668
and then inside, inside
of this little place

00:05:07.668 --> 00:05:11.914
right over here, you're going
to have a more fancy version

00:05:11.914 --> 00:05:14.554
of this rotating which is
going to induce a current.

00:05:14.554 --> 00:05:16.870
The magnetic field isn't
going to be exactly like this.

00:05:16.870 --> 00:05:18.659
It's going to be a more
sophisticated mechanism

00:05:18.659 --> 00:05:20.935
but it's the same underlying principle.

00:05:20.935 --> 00:05:22.743
It's just Faraday's law at work.

00:05:22.743 --> 00:05:24.754
Same thing with hydroelectric generator,

00:05:24.754 --> 00:05:26.400
you're using the potential energy

00:05:26.400 --> 00:05:30.890
of the flowing water to turn an axle

00:05:30.890 --> 00:05:32.983
and then that helps us
generate electricity

00:05:32.983 --> 00:05:36.335
by the exact same principle.


Emf induced in rod traveling through magnetic field

WEBVTT
Kind: captions
Language: en

00:00:00.767 --> 00:00:02.856
- [Voiceover] I have an
interesting set up over here.

00:00:02.856 --> 00:00:06.136
I have a magnetic field that is constant,

00:00:06.136 --> 00:00:11.136
and it's going straight out
of the surface of this loop.

00:00:11.454 --> 00:00:14.817
The magnitude of the magnetic field

00:00:14.817 --> 00:00:19.817
at any point of the
surface is going to be 'B'.

00:00:19.935 --> 00:00:23.782
What's interesting here
is this loop that we have,

00:00:23.782 --> 00:00:25.838
This right part of the loop is movable.

00:00:25.838 --> 00:00:27.358
You can imagine it's a cylinder

00:00:27.358 --> 00:00:29.613
that can roll to the right,

00:00:29.613 --> 00:00:31.235
and the magnitude of it's velocity,

00:00:31.235 --> 00:00:33.645
we're going to say is lowercase 'v'.

00:00:33.645 --> 00:00:37.830
And this cylinder, lets
say it has length 'L'

00:00:37.830 --> 00:00:39.687
Given that, you can see that we're going

00:00:39.687 --> 00:00:41.847
to have a change in magnetic flux.

00:00:41.847 --> 00:00:44.052
Why are we gonna have a
change in magnetic flux,

00:00:44.052 --> 00:00:46.235
or a change in magnetic
flux through the surface?

00:00:46.235 --> 00:00:51.235
Well if this thing is moving to the right,

00:00:51.506 --> 00:00:53.572
when it's speed is 'v'

00:00:53.572 --> 00:00:54.945
it can be any units, meters per second,

00:00:54.945 --> 00:00:56.170
or whatever it is.

00:00:56.170 --> 00:00:57.926
Even though the magnetic field itself is

00:00:57.926 --> 00:01:01.734
constant, you're actually
going to be changing the area,

00:01:01.734 --> 00:01:04.404
the area that is, I guess
you could, contained by

00:01:04.404 --> 00:01:06.563
this loop, and so that is going to

00:01:06.563 --> 00:01:08.073
give us a change in flux

00:01:08.073 --> 00:01:09.582
And if you have a change in flux that is

00:01:09.582 --> 00:01:14.582
going to induce an electromotive force,

00:01:15.688 --> 00:01:18.405
or it's going to induce
a voltage in this loop

00:01:18.405 --> 00:01:21.083
which will cause a current to flow.

00:01:21.083 --> 00:01:23.522
Let's think about what
that electromotive force

00:01:23.522 --> 00:01:25.603
that's going to be induced is going to be.

00:01:25.603 --> 00:01:28.552
I'm just gonna rewrite
Faraday's law right over here.

00:01:28.552 --> 00:01:31.053
Faradays law: negative 'N' times

00:01:31.053 --> 00:01:35.378
our change in flux, and we're talking

00:01:35.378 --> 00:01:40.168
about our change in flux over change in,

00:01:40.168 --> 00:01:41.689
let me write that a little bit neater,

00:01:41.689 --> 00:01:46.689
our change in flux over change in time.

00:01:49.627 --> 00:01:53.365
The 'N' is the number of
loops we're talking about.

00:01:53.365 --> 00:01:56.082
So in this case, 'N'
is just going to be one

00:01:56.082 --> 00:01:57.958
and the negative, I've already complained

00:01:57.958 --> 00:01:59.774
a little bit about in previous videos.

00:01:59.774 --> 00:02:01.654
This is really just reminding us

00:02:01.654 --> 00:02:05.996
the math, when you're not using
proper vector mathematics,

00:02:05.996 --> 00:02:08.628
this just reminds us that this 'Emf'

00:02:08.628 --> 00:02:11.796
is going to cause a current
to go through this loop,

00:02:11.796 --> 00:02:14.100
and the magnetic field that is

00:02:14.100 --> 00:02:16.840
induced by that current will
go against the direction

00:02:16.840 --> 00:02:21.840
of our change in flux. That's
just something to remind us.

00:02:23.457 --> 00:02:26.197
What we really care about is

00:02:26.197 --> 00:02:29.447
our change in flux over change in time.

00:02:29.447 --> 00:02:30.701
What is that going to be?

00:02:30.701 --> 00:02:31.630
Let me just write it here,

00:02:31.630 --> 00:02:36.630
our change in flux over change in time.

00:02:37.621 --> 00:02:39.664
Our change in flux in this case

00:02:39.664 --> 00:02:41.243
is going to be our change in

00:02:41.243 --> 00:02:44.442
our, the magnitude of our magnetic field

00:02:44.442 --> 00:02:46.142
that is going perpendicular to the surface

00:02:46.142 --> 00:02:50.182
times the area of our surface

00:02:50.182 --> 00:02:54.013
over our change in time.

00:02:54.013 --> 00:02:55.430
What is this going to be equal to?

00:02:55.430 --> 00:02:58.355
'B' is constant, it's not going to change

00:02:58.355 --> 00:02:59.679
over the time that we care about.

00:02:59.679 --> 00:03:01.304
So the change in 'B' times 'A'

00:03:01.304 --> 00:03:05.896
is really going to be 'B'
times our change in area.

00:03:05.896 --> 00:03:10.896
'B' times our change in area
over how much time goes by.

00:03:11.520 --> 00:03:14.028
So what is our change in area going to be?

00:03:14.028 --> 00:03:19.028
Let's say we let delta 't' ,
let's say delta 't' happens,

00:03:19.479 --> 00:03:22.943
what is going to be our change in area?

00:03:22.943 --> 00:03:24.796
Let's let delta 't' go on.

00:03:24.796 --> 00:03:27.490
If delta 't' goes on, this cylinder,

00:03:27.490 --> 00:03:31.731
or if we wait for 't' units of time,

00:03:31.731 --> 00:03:34.711
or if 't' units of time go by,

00:03:34.711 --> 00:03:39.711
let me do this in another color,

00:03:40.446 --> 00:03:45.446
I'm gonna use this color right over here.

00:03:45.554 --> 00:03:48.781
How far will we go after delta 't'?

00:03:48.781 --> 00:03:50.226
We know the magnitude of our velocity

00:03:50.226 --> 00:03:52.682
if you multiply the
magnitude of your velocity

00:03:52.682 --> 00:03:54.429
times your change in time,

00:03:54.429 --> 00:03:58.655
that will give you your distance.

00:03:58.655 --> 00:04:00.095
Your change in area is going to be

00:04:00.095 --> 00:04:02.270
the amount of distance it's travelled

00:04:02.270 --> 00:04:07.270
times the length of the
rod, which is just that.

00:04:08.355 --> 00:04:12.726
Our change in area, which is
that area right over there,

00:04:12.726 --> 00:04:17.039
our change in area over that time

00:04:17.039 --> 00:04:19.825
is going to be the distance this rod goes.

00:04:19.825 --> 00:04:22.170
Notice this rod is going in a direction

00:04:22.170 --> 00:04:26.002
that is perpendicular to the
direction of the magnetic field

00:04:26.002 --> 00:04:28.463
that's an important thing to realize.

00:04:28.463 --> 00:04:31.533
We have our change in area is going to be

00:04:31.533 --> 00:04:36.468
this dimension which is
how far the rod travels

00:04:36.468 --> 00:04:40.397
times the length of the rod,
that's how much area we gain,

00:04:40.397 --> 00:04:42.812
that's how much our area increases,

00:04:42.812 --> 00:04:47.758
times the length of the rod,
that's our change in area.

00:04:47.758 --> 00:04:50.503
We can substitute that back over here.

00:04:50.503 --> 00:04:55.503
This is going to be equal to,

00:04:55.590 --> 00:04:58.624
we got our 'B', we have
our change in time,

00:04:58.624 --> 00:05:02.734
and our change in area we
just said is going to be,

00:05:02.734 --> 00:05:03.709
Let me just write it this way,

00:05:03.709 --> 00:05:06.774
I could write is as the length of our rod

00:05:06.774 --> 00:05:10.048
times the magnitude of
our velocity, or our speed

00:05:10.048 --> 00:05:12.824
times our change in time.

00:05:12.824 --> 00:05:15.226
Well, change in time
divided by change in time,

00:05:15.226 --> 00:05:20.226
those cancel out. Our change
in flux over that time

00:05:21.959 --> 00:05:24.263
or our average rate of change in flux

00:05:24.263 --> 00:05:28.768
we see simplifies to the length of our rod

00:05:28.768 --> 00:05:31.304
times the magnitude of our velocity,

00:05:31.304 --> 00:05:35.548
or our speed, times the
magnitude of the magnetic field

00:05:35.548 --> 00:05:38.706
that is going perpendicular
to the surface.

00:05:38.706 --> 00:05:41.306
This is something that
you will see many times

00:05:41.306 --> 00:05:44.116
in your physics class,
this whole notion of

00:05:44.116 --> 00:05:46.711
if your rod going in a
perpendicular direction

00:05:46.711 --> 00:05:48.615
to a magnetic field, it induces

00:05:48.615 --> 00:05:51.494
an electromotive force of 'LvB'

00:05:51.494 --> 00:05:52.539
This is where it's coming from,

00:05:52.539 --> 00:05:55.604
it's coming directly from Faraday's law.

00:05:55.604 --> 00:05:57.810
You can say, okay, if that's happening,

00:05:57.810 --> 00:06:02.810
what direction is the current
going to actually flow in?

00:06:03.243 --> 00:06:06.408
If the magnetic field isn't changing,

00:06:06.408 --> 00:06:08.015
but since the area is increasing,

00:06:08.015 --> 00:06:12.357
the flux is increasing
in the upward direction.

00:06:12.357 --> 00:06:14.238
You can say the flux is
increasing in that direction.

00:06:14.238 --> 00:06:15.817
The current that gets induced,

00:06:15.817 --> 00:06:17.442
and the magnitude of the
current is going to be,

00:06:17.442 --> 00:06:19.642
based on how much resistance we have,

00:06:19.642 --> 00:06:22.916
but the current is going
to induce a magnetic field

00:06:22.916 --> 00:06:27.630
that goes against our change in flux.

00:06:27.630 --> 00:06:32.630
Let's see, if the current went
that way, what will happen?

00:06:35.733 --> 00:06:39.133
I'm going to take my right hand out,

00:06:39.133 --> 00:06:41.213
put my thumb in that direction,

00:06:41.213 --> 00:06:45.392
and if I were to loop my fingers around,

00:06:45.392 --> 00:06:49.043
this would, if we went that
way, this would describe,

00:06:49.043 --> 00:06:50.738
this would induce a magnetic field

00:06:50.738 --> 00:06:54.569
that goes like this.

00:06:54.569 --> 00:06:57.030
That actually would enhance

00:06:57.030 --> 00:06:59.004
the flux going through
the, or change in flux,

00:06:59.004 --> 00:07:00.931
going the same direction
of the change in flux,

00:07:00.931 --> 00:07:02.185
We've already talked about this,

00:07:02.185 --> 00:07:04.600
would violate the law of
conservation of energy.

00:07:04.600 --> 00:07:09.600
The current's gonna go
in the other direction.

00:07:10.871 --> 00:07:14.166
It's gonna go, in this case
is going to go clockwise,

00:07:14.166 --> 00:07:16.395
because the current is going
to induce a magnetic field.

00:07:16.395 --> 00:07:18.322
Once again, I could
take my right hand out,

00:07:18.322 --> 00:07:21.596
and try to draw my right hand,

00:07:21.596 --> 00:07:22.804
and we can see now, the direction

00:07:22.804 --> 00:07:25.631
my fingers go in are that way.

00:07:25.631 --> 00:07:27.656
Notice we're looking at
the inside of the surface,

00:07:27.656 --> 00:07:31.830
the surface area was increasing the flux

00:07:31.830 --> 00:07:35.365
in the upward direction, getting more

00:07:35.365 --> 00:07:38.276
of the magnetic field
in the upward direction,

00:07:38.276 --> 00:07:39.907
being contained in the area.

00:07:39.907 --> 00:07:43.854
The magnetic field induced by
the current that is induced,

00:07:43.854 --> 00:07:46.269
or that current that's being caused

00:07:46.269 --> 00:07:49.537
by the electromotive
force and the magnitude of

00:07:49.537 --> 00:07:51.232
the force is going to be
dependent on our resistance,

00:07:51.232 --> 00:07:52.788
that's going to go in the other direction,

00:07:52.788 --> 00:07:55.073
it's going to go down that way.

00:07:55.073 --> 00:07:56.735
Or it's going to induce a magnetic field

00:07:56.735 --> 00:07:58.709
that is gonna go downwards.

00:07:58.709 --> 00:08:00.709
So the current needs
to be going clockwise.


Faraday's Law example

WEBVTT
Kind: captions
Language: en

00:00:00.469 --> 00:00:02.401
- So we have something
interesting going on.

00:00:02.401 --> 00:00:05.821
I have this ring of conductor
right here, this square ring,

00:00:05.821 --> 00:00:09.733
it has a resistance of two
ohms, we see that it is

00:00:09.733 --> 00:00:12.682
two meters by two meters so the area

00:00:12.682 --> 00:00:15.723
of this ring would be four square meters

00:00:15.723 --> 00:00:18.324
and we see a magnetic field going through

00:00:18.324 --> 00:00:21.040
the surface defined by the
ring and it's constant,

00:00:21.040 --> 00:00:23.455
it's a constant magnetic
field of five teslas

00:00:23.455 --> 00:00:26.183
and it's going exactly perpendicularly to,

00:00:26.183 --> 00:00:30.362
perpendicularly to the
surface of the ring.

00:00:30.362 --> 00:00:32.962
Now what we're going to happen, what we're

00:00:32.962 --> 00:00:35.761
going to see happen is
over the next four seconds,

00:00:35.761 --> 00:00:38.744
and this is going to
happen at a linear rate,

00:00:38.744 --> 00:00:40.659
it's going to happen at a constant rate,

00:00:40.659 --> 00:00:43.120
we're going to see the magnetic
field over four seconds

00:00:43.120 --> 00:00:46.226
go from five teslas to 10
teslas so it's going to

00:00:46.226 --> 00:00:48.704
double over those four
seconds and by doing so

00:00:48.704 --> 00:00:50.573
we're going to have a change in flux.

00:00:50.573 --> 00:00:51.955
Let's think about what the change

00:00:51.955 --> 00:00:54.660
in flux is over this four seconds.

00:00:54.660 --> 00:00:57.875
So our initial flux, let
me write it over here,

00:00:57.875 --> 00:01:01.915
so flux, let me use a different color

00:01:01.915 --> 00:01:03.703
and at any time if you are so inspired

00:01:03.703 --> 00:01:04.957
I encourage you to pause the video

00:01:04.957 --> 00:01:07.679
and figure out what our change in flux is.

00:01:07.679 --> 00:01:11.785
So our flux, flux initial

00:01:11.785 --> 00:01:14.725
is going to be, well it's the

00:01:14.725 --> 00:01:16.937
it's going to be the
constant magnetic field,

00:01:16.937 --> 00:01:18.493
you could say the average magnetic field

00:01:18.493 --> 00:01:19.898
over the surface but since it's constant

00:01:19.898 --> 00:01:23.980
that's just going to be
five teslas, so five teslas

00:01:23.980 --> 00:01:25.818
and it helps for, it
helps us in this problem

00:01:25.818 --> 00:01:28.046
that the magnetic field
vectors are exactly

00:01:28.046 --> 00:01:30.555
perpendicular to the
surface, to the surface

00:01:30.555 --> 00:01:32.436
defined by the ring, if
they weren't we would

00:01:32.436 --> 00:01:35.013
have to find the component
that is perpendicular

00:01:35.013 --> 00:01:36.499
but we have that right
over there so we have

00:01:36.499 --> 00:01:38.739
the five teslas, that's
the average magnetic field

00:01:38.739 --> 00:01:41.558
or the average component
of the magnetic field

00:01:41.558 --> 00:01:43.990
that is perpendicular to the surface,

00:01:43.990 --> 00:01:46.680
so five teslas times
the area of the surface.

00:01:46.680 --> 00:01:50.969
So times, well two meters
times two meters is four

00:01:50.969 --> 00:01:55.509
square meters so that
is going to be equal to,

00:01:55.509 --> 00:01:58.470
that is equal to 20

00:01:58.470 --> 00:02:01.180
tesla meter squared,

00:02:01.180 --> 00:02:05.051
tesla meter squared, fair enough.

00:02:05.051 --> 00:02:08.858
Now what's the final,
what's the final flux?

00:02:08.858 --> 00:02:13.641
The final flux, flux final
is going to be equal to,

00:02:13.641 --> 00:02:16.695
well now the average magnetic field or

00:02:16.695 --> 00:02:18.332
the average components
of the magnetic field

00:02:18.332 --> 00:02:19.460
that are perpendicular in the way

00:02:19.460 --> 00:02:20.486
I've defined this magnetic field,

00:02:20.486 --> 00:02:22.388
the vectors are already perpendicular

00:02:22.388 --> 00:02:26.078
is 10 teslas, so 10 teslas.

00:02:26.078 --> 00:02:29.048
The area of our ring hasn't changed,

00:02:29.048 --> 00:02:31.741
it's still four square meters,

00:02:31.741 --> 00:02:34.552
so times four square meters,

00:02:34.552 --> 00:02:36.653
and so what is this going to be?

00:02:36.653 --> 00:02:40.870
So our final flux is going to be

00:02:40.870 --> 00:02:44.422
final flux is going to be 40,

00:02:44.422 --> 00:02:48.590
40 tesla meters squared.

00:02:48.590 --> 00:02:52.003
So what is our, what
is our change in flux?

00:02:52.003 --> 00:02:56.471
Let me write this over here,
our change in flux, change in

00:02:56.471 --> 00:03:00.381
flux, which is going to be our final flux

00:03:01.161 --> 00:03:05.667
minus our initial flux is going to be

00:03:05.667 --> 00:03:09.149
40 tesla meters squared minus
20 tesla meters squared,

00:03:09.149 --> 00:03:13.863
which is just going to be
20 tesla meters squared.

00:03:14.223 --> 00:03:16.846
So we figured out the change
in flux, we actually know

00:03:16.846 --> 00:03:19.319
the change in time is
going to be four seconds

00:03:19.319 --> 00:03:22.001
and actually using that
we can now figure out

00:03:22.001 --> 00:03:24.857
what the voltage induced is going to be,

00:03:24.857 --> 00:03:27.306
the voltage induced, or
the voltage that's going

00:03:27.306 --> 00:03:29.814
to now induce, induce a current.

00:03:29.814 --> 00:03:32.809
And if you were to look up
Faraday's law on the internet,

00:03:32.809 --> 00:03:34.991
you were to look up for a
formula for Faraday's law

00:03:34.991 --> 00:03:36.693
you would see something
that looks like this,

00:03:36.693 --> 00:03:39.963
you would see voltage
generated is equal to

00:03:39.963 --> 00:03:42.797
negative and, at least
if you're not using the

00:03:42.797 --> 00:03:47.797
calculus version of it, negative
N times our change in flux,

00:03:47.799 --> 00:03:51.897
change in, let me write
change in flux not just flux,

00:03:51.897 --> 00:03:54.889
change in flux, delta flux

00:03:54.889 --> 00:03:57.599
over change in time.

00:03:57.599 --> 00:04:00.112
So one way to think about
this, and to do this problem

00:04:00.112 --> 00:04:02.357
right we're assuming we have a constant

00:04:02.357 --> 00:04:05.267
or the rate of change
is constant in our flux

00:04:05.267 --> 00:04:09.040
so you have your average
rate of change of your flux

00:04:09.040 --> 00:04:11.617
and then you're going
to multiply it times N.

00:04:11.617 --> 00:04:14.086
N is actually the number of
loops you have, or you can

00:04:14.086 --> 00:04:16.562
think of it as the number
of surfaces defined by it.

00:04:16.562 --> 00:04:19.198
In this exact example,
in this exact example

00:04:19.198 --> 00:04:21.380
N is just going to be
one, we just have one loop

00:04:21.380 --> 00:04:23.563
so that simplifies it right over there

00:04:23.563 --> 00:04:25.803
and then, so this is going
to be, and you might say

00:04:25.803 --> 00:04:27.359
what is this negative
because it's a bit of

00:04:27.359 --> 00:04:29.210
a strange thing because
you know, how are we

00:04:29.210 --> 00:04:30.935
defining direction, you
know what's in the--

00:04:30.935 --> 00:04:33.530
and all of that and that's
why I'm a little bit,

00:04:33.530 --> 00:04:35.625
I'm not a huge fan of this negative sign.

00:04:35.625 --> 00:04:38.063
This is, you know if you
look it up in a textbook

00:04:38.063 --> 00:04:39.920
they'll often say, and
you're not using calculus,

00:04:39.920 --> 00:04:42.579
they'll say, oh this
reminder to use Lenz's law,

00:04:42.579 --> 00:04:45.424
they'll write literally Lenz's law

00:04:45.424 --> 00:04:47.013
and I would say if they
want a reminder to use

00:04:47.013 --> 00:04:48.337
Lenz's law why don't they just remind you

00:04:48.337 --> 00:04:50.159
to use Lenz's law instead of putting

00:04:50.159 --> 00:04:51.982
a kind of bizarre negative sign there.

00:04:51.982 --> 00:04:53.619
And the negative sign
actually does make sense

00:04:53.619 --> 00:04:56.574
if you were, if you were doing kind of the

00:04:56.574 --> 00:04:58.947
using the vectors here and taking the,

00:04:58.947 --> 00:05:00.607
and using a little bit of the,

00:05:00.607 --> 00:05:03.405
well, doing more sophisticated mathematics

00:05:03.405 --> 00:05:05.831
but this is just saying
that the voltage induced

00:05:05.831 --> 00:05:08.002
is going to be in a direction so to

00:05:08.002 --> 00:05:11.004
induce a current whose, whose induced

00:05:11.004 --> 00:05:13.275
magnetic field will go in the direction,

00:05:13.275 --> 00:05:15.746
will counteract the change in flux,

00:05:15.746 --> 00:05:17.510
so that's just Lenz's law there.

00:05:17.510 --> 00:05:19.903
So the real key here, at
least for this example

00:05:19.903 --> 00:05:22.142
is to find our change in
flux over change in time

00:05:22.142 --> 00:05:25.068
or our average, our average
rate of change in flux

00:05:25.068 --> 00:05:26.600
and what is this going to be?

00:05:26.600 --> 00:05:29.769
Well this is going to be
20 tesla meters squared,

00:05:29.769 --> 00:05:34.312
20 tesla meters squared,
that was our change in flux

00:05:34.762 --> 00:05:37.362
right over there divided
by our change in time,

00:05:37.362 --> 00:05:41.008
which is four seconds, over four seconds,

00:05:41.008 --> 00:05:42.829
which is going to be equal to, and I'll,

00:05:42.829 --> 00:05:45.295
I could throw that negative
there if we want to,

00:05:45.295 --> 00:05:49.475
that negative 20 divided by four is five,

00:05:50.445 --> 00:05:55.228
five tesla meters squared or square meters

00:05:55.228 --> 00:05:59.904
per second and this actually
turns out to be a volt,

00:05:59.904 --> 00:06:02.576
so we could say this
is negative five volts,

00:06:02.576 --> 00:06:05.991
negative, negative five volts,

00:06:07.511 --> 00:06:09.462
negative five volts.

00:06:09.462 --> 00:06:13.223
So if you have a voltage of,
well let's just say five volts,

00:06:13.223 --> 00:06:15.266
we can think about the negative later,

00:06:15.266 --> 00:06:18.545
if you have a voltage
of five volts across a,

00:06:18.545 --> 00:06:22.162
across a circuit that has
a resistance of two ohms

00:06:22.162 --> 00:06:25.529
what is the current, what
is the current going to be?

00:06:25.529 --> 00:06:27.665
Well we just have to remind ourselves

00:06:27.665 --> 00:06:30.288
V is equal to I-R

00:06:30.288 --> 00:06:32.842
or voltage is equal to
the current divided by

00:06:32.842 --> 00:06:34.584
the resistance, or voltage is equal to

00:06:34.584 --> 00:06:37.444
the current times the
resistance or you could say

00:06:37.444 --> 00:06:41.151
that the current, the current is equal to

00:06:41.151 --> 00:06:43.461
the voltage divided by the resistance.

00:06:43.461 --> 00:06:46.351
So in this case the
current, the current induced

00:06:46.351 --> 00:06:47.570
is going to be the voltage
and I'm just going to

00:06:47.570 --> 00:06:49.172
focus on its absolute value now, we can

00:06:49.172 --> 00:06:51.053
think about its direction in a second.

00:06:51.053 --> 00:06:53.132
It's going to be its voltage, five volts

00:06:53.132 --> 00:06:57.032
divided by the resistance, so two ohms,

00:06:57.032 --> 00:07:01.757
two ohms, which is going to be equal to,

00:07:01.757 --> 00:07:06.418
this is going to be equal to 2.5, 2.5

00:07:06.418 --> 00:07:10.974
amperes, 2.5 amperes.

00:07:11.914 --> 00:07:13.865
So we now know the
magnitude of the current

00:07:13.865 --> 00:07:15.316
that's going to be induced while we

00:07:15.316 --> 00:07:16.744
have this change in flux, remember this

00:07:16.744 --> 00:07:18.961
is going to happen while, over the course

00:07:18.961 --> 00:07:21.724
of those four seconds, as
we have this rate of change

00:07:21.724 --> 00:07:24.139
of flux, this average
rate of change of flux,

00:07:24.139 --> 00:07:26.716
which we'll assume is the
actual rate of change of flux,

00:07:26.716 --> 00:07:30.257
we're assuming that it's
changing at a constant rate

00:07:30.257 --> 00:07:32.777
and so while it is changing we
were just able to figure out

00:07:32.777 --> 00:07:36.398
that it would induce a
current of 2.5 amperes.

00:07:36.398 --> 00:07:37.954
Now the next question
we should ask ourselves

00:07:37.954 --> 00:07:40.020
and this is where this
little negative comes in,

00:07:40.020 --> 00:07:43.015
is a reminder for us to
use Lenz's law is, well

00:07:43.015 --> 00:07:45.256
which direction is that
current going to go in?

00:07:45.256 --> 00:07:48.135
Is it going to go in, let
me pick two orientations,

00:07:48.135 --> 00:07:52.279
is it going to go in a,
is it going to go in a,

00:07:52.279 --> 00:07:56.853
in a clockwise direction,
is it going to go that way

00:07:56.853 --> 00:07:59.451
over the course of this change in flux

00:07:59.451 --> 00:08:01.450
or is it going to go in a
counterclockwise direction,

00:08:01.450 --> 00:08:03.609
is it going to go that way?

00:08:03.609 --> 00:08:05.316
And to think about that
we just have to use

00:08:05.316 --> 00:08:07.615
the right hand rule, take our right hand,

00:08:07.615 --> 00:08:08.729
point our thumb in the direction

00:08:08.729 --> 00:08:12.850
of the proposed direction of the current

00:08:12.850 --> 00:08:15.636
and so if we went with
this one, our right hand,

00:08:15.636 --> 00:08:17.169
our right hand would look like this,

00:08:17.169 --> 00:08:19.758
I'm literally taking
my left hand out and--

00:08:19.758 --> 00:08:22.753
I mean my right hand
out and I'm drawing it

00:08:22.753 --> 00:08:25.411
and I'm looking at it to
think about what would happen,

00:08:25.411 --> 00:08:27.954
so that's my right hand
so if I use the right hand

00:08:27.954 --> 00:08:29.718
if the current went in this
direction then it would

00:08:29.718 --> 00:08:33.539
induce a magnetic field that went,

00:08:33.539 --> 00:08:36.022
that went like this and
so if the current went

00:08:36.022 --> 00:08:38.448
in this direction the
magnetic field it induces

00:08:38.448 --> 00:08:42.511
inside the surface would only
reinforce the change in flux

00:08:42.511 --> 00:08:45.541
so it would only add to
the flux so, and it's going

00:08:45.541 --> 00:08:47.445
in the same direction
as the change in flux,

00:08:47.445 --> 00:08:49.629
which would just keep us, you know as we

00:08:49.629 --> 00:08:51.985
talked about in the Lenz's law video,

00:08:51.985 --> 00:08:54.921
that would turn into just
this source of energy

00:08:54.921 --> 00:08:56.991
that comes out of nowhere and defies

00:08:56.991 --> 00:08:59.391
the law of conservation of energy so this

00:08:59.391 --> 00:09:01.632
absolutely not, is not
going to be the direction

00:09:01.632 --> 00:09:03.129
and so we know that the direction

00:09:03.129 --> 00:09:06.391
is going to be in a clockwise one.

00:09:06.391 --> 00:09:10.049
So the current, the 2.5 ampere current

00:09:10.049 --> 00:09:14.936
is going to flow, is
going to flow like that,

00:09:14.936 --> 00:09:15.982
and we're done!

00:09:15.982 --> 00:09:17.768
By thinking about our change in flux

00:09:17.768 --> 00:09:20.811
and how long it's taking us,
we were able to figure out

00:09:20.811 --> 00:09:22.873
not only the magnitude of
the current, we were able

00:09:22.873 --> 00:09:24.826
to figure out the
orientation of the direction

00:09:24.826 --> 00:09:26.817
that it's actually going to flow in.


Lenz's Law

WEBVTT
Kind: captions
Language: en

00:00:00.317 --> 00:00:01.684
- So, right over here depicted

00:00:01.684 --> 00:00:04.101
a square loop of a conductor.

00:00:04.101 --> 00:00:05.874
Let's say it's a wire and it's stationary

00:00:05.874 --> 00:00:07.645
and it's sitting in a magnetic field.

00:00:07.807 --> 00:00:10.004
And I've drawn a few
vectors that represent

00:00:10.004 --> 00:00:12.350
the magnetic field and
you can see at least on

00:00:12.350 --> 00:00:15.399
the surface that is defined
or that is contoured

00:00:15.529 --> 00:00:19.198
by the wire that the magnetic
field looks constant.

00:00:19.198 --> 00:00:20.434
So, if we just had this scenario

00:00:20.434 --> 00:00:22.291
nothing too special going on

00:00:22.291 --> 00:00:25.508
but it becomes interesting
if I were to actually change

00:00:25.508 --> 00:00:28.435
the flux going through the surface.

00:00:28.616 --> 00:00:30.351
So, both of these pictures right over here

00:00:30.351 --> 00:00:32.385
they actually show the same scenario

00:00:32.505 --> 00:00:35.067
where we have increased the flux.

00:00:35.151 --> 00:00:37.749
We have increased the flux at these points

00:00:37.749 --> 00:00:41.619
on the surface defined by
the wire at every point

00:00:41.619 --> 00:00:44.178
the magnetic field has
now gotten stronger.

00:00:44.178 --> 00:00:46.384
So, we have increased the flux.

00:00:46.384 --> 00:00:48.015
So, let me write that, the flux.

00:00:48.015 --> 00:00:51.017
We use the Greek letter
phi used to denote flux.

00:00:51.017 --> 00:00:53.967
The flux of the magnetic field.

00:00:54.518 --> 00:00:57.400
The flux of the magnetic
field has gone up.

00:00:57.952 --> 00:01:00.417
And we know from Faraday's law

00:01:00.417 --> 00:01:02.350
that when you have a change in your flux

00:01:02.350 --> 00:01:06.420
that that's going to induce
a current in the loop.

00:01:06.684 --> 00:01:08.531
And so an interesting question is

00:01:08.531 --> 00:01:11.538
what direction is that current
actually going to go in?

00:01:11.651 --> 00:01:13.019
We have two options.

00:01:13.019 --> 00:01:15.031
The current could go.

00:01:15.151 --> 00:01:17.762
The current... Let me find a
nice color for the current.

00:01:17.762 --> 00:01:22.762
The current could go in
the clockwise direction

00:01:24.098 --> 00:01:28.651
or it could go in the
counter clockwise direction.

00:01:28.651 --> 00:01:30.351
So, which of these two do you think

00:01:30.351 --> 00:01:32.069
the current will actually go with?

00:01:32.643 --> 00:01:33.917
Well, let's think a little bit about it.

00:01:33.917 --> 00:01:35.684
We know that a current flowing through

00:01:35.684 --> 00:01:40.051
a wire actually on it's own
will induce a magnetic field

00:01:40.051 --> 00:01:42.201
above and beyond a magnet
field that's already there.

00:01:42.617 --> 00:01:44.785
So, let's think about the
type of magnetic field

00:01:44.785 --> 00:01:48.119
that this orange current
would actually induce.

00:01:48.484 --> 00:01:51.194
So, if it's going in the
counter clockwise direction

00:01:51.194 --> 00:01:53.284
remember we use the right hand rule.

00:01:53.284 --> 00:01:55.251
I can take my right hand

00:01:55.251 --> 00:01:57.990
point my thumb in the
direction of the current.

00:01:57.990 --> 00:01:59.418
So, let me see if I can do that.

00:01:59.418 --> 00:02:01.552
So, my thumb in the
direction of the current

00:02:01.552 --> 00:02:05.722
and then my hands are going to loop

00:02:05.722 --> 00:02:07.851
or I should say my
fingers are going to loop

00:02:07.851 --> 00:02:10.864
in the direction of the magnetic field.

00:02:10.864 --> 00:02:12.491
So, when I do that with my right hand,

00:02:12.491 --> 00:02:14.331
so my right hand looks
something like that thumb

00:02:14.331 --> 00:02:16.751
in the direction of the
current right over here

00:02:16.751 --> 00:02:19.881
we see that it shows the
magnetic field being induced

00:02:20.111 --> 00:02:22.237
that would wrap around like that.

00:02:22.484 --> 00:02:23.825
Or if we were to show
it, if we were to sample

00:02:23.825 --> 00:02:25.781
it points right on the surface

00:02:26.151 --> 00:02:28.285
the magnetic field that would be induced

00:02:28.285 --> 00:02:29.964
would look something like this

00:02:30.084 --> 00:02:32.222
and I'm just doing it
at some sample points.

00:02:32.351 --> 00:02:37.351
So, notice it would be additive

00:02:41.481 --> 00:02:43.218
to the existing magnetic field.

00:02:43.218 --> 00:02:45.181
In fact, it would increase
the flux even more.

00:02:45.181 --> 00:02:47.268
In fact, at these points these vectors

00:02:47.268 --> 00:02:48.634
would increase even more.

00:02:48.884 --> 00:02:51.700
These vectors, let me
see if I can draw that.

00:02:51.718 --> 00:02:53.635
These vectors would increase even more.

00:02:53.784 --> 00:02:54.574
Well, what would that do?

00:02:54.574 --> 00:02:55.751
If the flux increases even more

00:02:55.751 --> 00:02:57.617
then the current is going to increase.

00:02:57.617 --> 00:02:59.517
The current is going to increase even more

00:02:59.517 --> 00:03:01.260
which is going to make the
flux increase even more

00:03:01.260 --> 00:03:02.752
and which makes the
current increase even more

00:03:02.752 --> 00:03:04.918
and you would have this never ending cycle

00:03:04.918 --> 00:03:06.116
where the current keeps increasing,

00:03:06.116 --> 00:03:08.284
the flux keeps increasing
and you would have

00:03:08.284 --> 00:03:10.484
this energy that's
appearing out of nowhere

00:03:10.484 --> 00:03:13.168
which would violate the law
of conservation of energy.

00:03:13.719 --> 00:03:15.818
And so that's a pretty good argument

00:03:15.818 --> 00:03:17.555
for why you would not...

00:03:17.851 --> 00:03:19.848
That's a pretty good
argument for why we would

00:03:19.848 --> 00:03:24.531
not expect the counter clockwise scenario.

00:03:24.531 --> 00:03:26.784
We would not want the
current that's been induced

00:03:26.784 --> 00:03:29.284
to induce a magnetic
field that goes in the

00:03:29.284 --> 00:03:32.535
same direction as our increase in flux.

00:03:32.851 --> 00:03:34.683
So, just by deductive reasoning we know

00:03:34.683 --> 00:03:36.484
that this is going to be the scenario

00:03:36.484 --> 00:03:37.854
and let's see if we think
about what happens here.

00:03:37.854 --> 00:03:39.304
We can do the right hand rule again.

00:03:39.304 --> 00:03:40.994
We take our right hand

00:03:40.994 --> 00:03:43.087
point our thumb in the
direction of the current

00:03:43.747 --> 00:03:45.327
point our thumb in the
direction of the current

00:03:45.327 --> 00:03:49.368
and we see if we do that
with our right hand.

00:03:49.551 --> 00:03:52.818
Well, now this would
induce a magnetic field

00:03:52.818 --> 00:03:55.034
that would decrease the flux.

00:03:55.085 --> 00:03:57.518
So, it would produce a magnetic field.

00:03:57.518 --> 00:03:58.650
The current right over here would produce

00:03:58.650 --> 00:04:01.416
a magnetic field that's going downward.

00:04:01.416 --> 00:04:03.638
The current in that direction would also

00:04:03.768 --> 00:04:06.264
when you take your right hand

00:04:06.264 --> 00:04:07.918
and you were to put it along here.

00:04:07.918 --> 00:04:12.404
Once again if you're going
in the counter clockwise,

00:04:12.404 --> 00:04:14.541
or sorry if you're going
in the clockwise direction

00:04:14.541 --> 00:04:16.584
over here that too when you do your

00:04:16.584 --> 00:04:17.784
right hand rule right over here

00:04:17.784 --> 00:04:20.374
your fingers would coil around that way.

00:04:20.374 --> 00:04:22.551
And so once again when
you look at the surface

00:04:22.551 --> 00:04:26.351
it would produce, it would
induce a magnetic field

00:04:26.351 --> 00:04:28.134
that is going in that direction.

00:04:28.217 --> 00:04:31.285
And so it would have the
induced magnetic field

00:04:31.285 --> 00:04:33.907
from the induced current will go against

00:04:33.907 --> 00:04:35.467
the change in flux.

00:04:35.485 --> 00:04:37.985
And this makes sense because
we won't go into this

00:04:37.985 --> 00:04:39.751
never ending positive feedback loop where

00:04:39.751 --> 00:04:41.117
the current keeps getting
strong and stronger

00:04:41.117 --> 00:04:42.550
and the flux keeps increasing

00:04:42.550 --> 00:04:44.167
and increasing and increasing.

00:04:44.718 --> 00:04:47.585
And this idea that the orientation

00:04:47.585 --> 00:04:49.191
of the current that is induced

00:04:49.191 --> 00:04:51.178
will produce a magnetic field

00:04:51.178 --> 00:04:54.751
that counter acts the change in flux.

00:04:54.751 --> 00:04:56.544
This is Lenz's law.

00:04:57.351 --> 00:05:00.591
Lenz's Law.

00:05:01.016 --> 00:05:03.291
And once again if that wasn't true

00:05:03.291 --> 00:05:04.518
then you would have a violation

00:05:04.518 --> 00:05:07.535
of the conservation of energy.

00:05:07.684 --> 00:05:10.565
So, in general if someone says okay well,

00:05:10.815 --> 00:05:12.184
this is the change in flux

00:05:12.184 --> 00:05:13.735
is happening in a certain direction.

00:05:14.018 --> 00:05:15.418
Well, to think about which way

00:05:15.418 --> 00:05:17.448
the current would flow
you just have to say

00:05:17.448 --> 00:05:19.614
well what type of a magnetic field

00:05:19.614 --> 00:05:22.117
would each direction
of the current produce?

00:05:22.117 --> 00:05:24.234
And that magnetic field
should go in a direction

00:05:24.234 --> 00:05:26.385
that goes against your change in flux.

00:05:26.385 --> 00:05:28.017
So, if the flux is increasing

00:05:28.017 --> 00:05:29.484
the magnetic field that's induced

00:05:29.484 --> 00:05:32.269
by the induced current should
make the flux decrease.

00:05:32.884 --> 00:05:34.518
If the flux was decreasing

00:05:34.518 --> 00:05:36.218
then the induced magnetic field

00:05:36.218 --> 00:05:37.828
by the induced current should make

00:05:37.828 --> 00:05:39.474
the flux decrease less

00:05:39.474 --> 00:05:43.821
or should be additive to the flux.


Faraday's Law Introduction

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:01.765
- [Voiceover] In other
videos we talk about

00:00:01.765 --> 00:00:04.409
how a current flowing through a wire

00:00:04.409 --> 00:00:07.257
can induce a magnetic field.

00:00:07.257 --> 00:00:09.186
And we're going to talk
about in this video

00:00:09.186 --> 00:00:10.974
is how we can go the other way.

00:00:10.974 --> 00:00:13.134
How a change in a magnetic field

00:00:13.134 --> 00:00:15.594
can affect or induce a current

00:00:15.594 --> 00:00:18.010
in a loop of wire.

00:00:18.010 --> 00:00:20.693
So we're gonna be going from a change,

00:00:20.693 --> 00:00:23.085
change in and actually we're gonna

00:00:23.085 --> 00:00:25.239
focus on magnetic flux.

00:00:27.268 --> 00:00:29.946
Magnetic flux through a loop.

00:00:31.924 --> 00:00:33.944
Through a loop.

00:00:33.944 --> 00:00:35.385
And we're going to see how this

00:00:35.385 --> 00:00:38.838
actually induces a current in that loop.

00:00:38.838 --> 00:00:43.022
So it induces a current.

00:00:43.022 --> 00:00:44.550
Induced current.

00:00:45.368 --> 00:00:46.716
So this right over here,

00:00:46.716 --> 00:00:49.282
and this is my attempt at
drawing a magnetic field,

00:00:49.282 --> 00:00:51.103
and these are the magnetic field lines.

00:00:51.103 --> 00:00:52.292
They don't look like lines because

00:00:52.292 --> 00:00:54.008
they're all popping out of the screen.

00:00:54.008 --> 00:00:56.840
They're moving towards
you, towards the viewer,

00:00:56.840 --> 00:01:00.440
so you can view these as
the tips of the arrow.

00:01:00.440 --> 00:01:02.203
And there's different ways
of showing magnetic fields.

00:01:02.203 --> 00:01:04.388
You could show magnetic
field lines like this.

00:01:04.388 --> 00:01:05.968
You could also use vectors.

00:01:05.968 --> 00:01:07.776
And when you're using field lines,

00:01:07.776 --> 00:01:09.564
it's the density of the field lines

00:01:09.564 --> 00:01:11.771
tell you how strong the magnetic field is.

00:01:11.771 --> 00:01:14.047
So if you go to the right
here, they are less dense.

00:01:14.047 --> 00:01:16.251
And so the magnetic field is less strong

00:01:16.251 --> 00:01:17.971
on the right-hand side over here

00:01:17.971 --> 00:01:20.291
than they are on the left-hand side,

00:01:20.291 --> 00:01:23.143
or at least that's what
I'm trying to depict.

00:01:23.143 --> 00:01:24.046
Now if we did it with vectors,

00:01:24.046 --> 00:01:25.791
we would have a bigger arrows pointing out

00:01:25.791 --> 00:01:28.274
over here than we would over there.

00:01:28.274 --> 00:01:30.505
But now let's do a loop of,

00:01:30.505 --> 00:01:32.085
let's do a loop of wire.

00:01:32.085 --> 00:01:34.606
So let me draw a loop of wire here.

00:01:34.606 --> 00:01:37.954
So let's say I have a
loop of wire that is,

00:01:37.954 --> 00:01:39.967
so this is my loop of wire.

00:01:41.321 --> 00:01:44.323
My loop of wire.

00:01:44.323 --> 00:01:46.125
So if I just throw that loop of wire,

00:01:46.125 --> 00:01:48.425
and it it's just stationary,
it's in this magnetic field,

00:01:48.425 --> 00:01:49.913
and the magnetic field isn't changing,

00:01:49.913 --> 00:01:53.489
I do have some flux
going through the I guess

00:01:53.489 --> 00:01:55.392
you could say the surface
defined by this wire,

00:01:55.392 --> 00:01:57.804
and if you're unfamiliar
with the term magnetic flux,

00:01:57.804 --> 00:02:00.568
I encourage you to watch
the video on magnetic flux.

00:02:00.568 --> 00:02:02.428
But if I just have this wire stationary

00:02:02.428 --> 00:02:05.816
in the magnetic field
nothing is going to happen.

00:02:05.816 --> 00:02:08.432
But I will be able to induce a current

00:02:08.432 --> 00:02:11.186
if I change the magnetic flux

00:02:11.186 --> 00:02:14.574
going through this surface in some way.

00:02:14.574 --> 00:02:16.829
So for example, right
now the magnetic field

00:02:16.829 --> 00:02:19.589
is pointing out of the screen.

00:02:19.589 --> 00:02:21.309
If I were to make it even stronger

00:02:21.309 --> 00:02:24.977
than the direction
pointing out of the screen,

00:02:24.977 --> 00:02:28.383
so I guess one way to think about it is

00:02:28.383 --> 00:02:30.441
if the change in the magnetic field,

00:02:30.441 --> 00:02:32.041
the change in the flux were to get

00:02:32.041 --> 00:02:34.829
even stronger in the outward direction,

00:02:34.829 --> 00:02:36.081
so I don't know a good way to,

00:02:36.081 --> 00:02:38.497
so it's gonna get even stronger
in the outer direction,

00:02:38.497 --> 00:02:39.936
I'll draw a big arrow there,

00:02:39.936 --> 00:02:41.912
I guess you could say that these things

00:02:41.912 --> 00:02:44.904
became even denser in
this outward direction,

00:02:44.904 --> 00:02:47.925
it is actually going to induce a current.

00:02:47.925 --> 00:02:49.875
And the current that it will induce

00:02:51.536 --> 00:02:53.145
is going to go in that direction.

00:02:53.145 --> 00:02:55.072
And now let me draw a little bit clearer.

00:02:55.072 --> 00:02:57.557
The current is going to
go in that direction.

00:02:57.557 --> 00:03:01.481
It's going to go in a clockwise
direction around this.

00:03:01.481 --> 00:03:03.104
And that is because that change

00:03:03.104 --> 00:03:06.521
in the magnetic flux
that induces a voltage,

00:03:06.521 --> 00:03:08.264
an electro mode of force

00:03:08.264 --> 00:03:10.495
that causes this current to flow,

00:03:13.001 --> 00:03:15.861
And there's other ways to
change the magnetic flux.

00:03:16.961 --> 00:03:19.373
If I were to lessen the magnetic field

00:03:19.373 --> 00:03:20.977
in the outward direction or another way,

00:03:20.977 --> 00:03:23.601
if the change in the
magnetic field were inwards,

00:03:23.601 --> 00:03:25.621
then the current would
go the other direction.

00:03:25.621 --> 00:03:28.439
But the key here is when I change the flux

00:03:29.399 --> 00:03:32.314
through this surface defined by this wire,

00:03:32.314 --> 00:03:34.241
it's going to induce a current.

00:03:34.241 --> 00:03:36.433
The current isn't going to be there

00:03:36.433 --> 00:03:37.637
if the magnetic field is stationary

00:03:37.637 --> 00:03:41.029
and I'm not changing this loop in any way,

00:03:41.029 --> 00:03:43.605
but as soon as I change
the flux in some way,

00:03:43.605 --> 00:03:45.673
I am going to induce a current.

00:03:45.673 --> 00:03:48.713
I could also, instead
of changing the field,

00:03:50.623 --> 00:03:52.825
I could actually move my coil,

00:03:52.825 --> 00:03:53.960
I could move it that way.

00:03:53.960 --> 00:03:55.216
And if I were to move it that way,

00:03:55.216 --> 00:03:58.653
the flux going through this surface,

00:03:58.653 --> 00:04:01.556
or I guess coming out of
this surface, will increase.

00:04:01.556 --> 00:04:02.972
Because if I move this to the left,

00:04:02.972 --> 00:04:06.452
the magnetic field is denser,
I guess it's stronger,

00:04:06.452 --> 00:04:08.984
so there will more flux
through this area here.

00:04:08.984 --> 00:04:10.174
So if you move it that way,

00:04:10.174 --> 00:04:12.054
you also would have a current like this.

00:04:12.054 --> 00:04:13.538
Now if you moved it the other way,

00:04:13.538 --> 00:04:16.026
if it was on the left-hand
side and you moved it that way,

00:04:16.026 --> 00:04:17.718
it would also induce a current,

00:04:17.718 --> 00:04:19.301
but now since the flux is lessening

00:04:19.301 --> 00:04:20.745
in the outward direction,

00:04:20.745 --> 00:04:23.045
the current would go in the other way.

00:04:23.045 --> 00:04:24.253
Now there's other ways to change the flux.

00:04:24.253 --> 00:04:26.294
You could actually change the area

00:04:26.294 --> 00:04:28.826
of this actual loop if somehow it was made

00:04:28.826 --> 00:04:32.804
out of some maybe stretchy wire somehow.

00:04:36.055 --> 00:04:38.555
If you had increased,
let me draw it this way.

00:04:39.537 --> 00:04:42.689
If you were somehow able to stretch it,

00:04:45.391 --> 00:04:49.180
so it contains, so the
actual area increases,

00:04:50.211 --> 00:04:51.531
if you were able to stretch it out

00:04:51.531 --> 00:04:53.134
so that the actual area increases,

00:04:53.134 --> 00:04:55.110
which would cause the flux in the out

00:04:55.110 --> 00:04:57.892
of the screen direction
to increase even more,

00:04:59.882 --> 00:05:02.005
that also would induce the current.

00:05:02.005 --> 00:05:04.910
And so this whole idea of a change

00:05:04.910 --> 00:05:07.974
in magnetic flux inducing a current,

00:05:07.974 --> 00:05:10.066
this is the essence and we'll go deeper

00:05:10.066 --> 00:05:11.551
into it in future videos,

00:05:11.551 --> 00:05:15.217
this is the essence of Faraday's Law.

00:05:20.191 --> 00:05:21.125
Faraday's Law.

00:05:21.125 --> 00:05:23.585
And we'll quantify this
more in future videos,

00:05:23.585 --> 00:05:25.139
but it's just the notion

00:05:25.139 --> 00:05:27.536
that if I have a loop of wire,

00:05:27.536 --> 00:05:29.579
and I have a changing magnetic flux

00:05:29.579 --> 00:05:31.391
through the loop of wire,

00:05:31.391 --> 00:05:34.908
that is going to induce
a current in that wire.