Electricity and magnetism
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Electrostatics (part 1): Introduction to Charge and Coulomb's Law
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Electrostatics (part 2)
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Proof (Advanced): Field from infinite plate (part 1)
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Proof (Advanced): Field from infinite plate (part 2)
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Electric Potential Energy
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Electric Potential Energy (part 2-- involves calculus)
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Voltage
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Capacitance
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Circuits (part 1)
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Circuits (part 2)
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Circuits (part 3)
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Circuits (part 4)
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Cross product 1
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Cross Product 2
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Cross Product and Torque
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Introduction to Magnetism
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Magnetism 2
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Magnetism 3
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Magnetism 4
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Magnetism 5
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Magnetism 6: Magnetic field due to current
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Magnetism 7
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Magnetism 8
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Magnetism 9: Electric Motors
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Magnetism 10: Electric Motors
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Magnetism 11: Electric Motors
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Magnetism 12: Induced Current in a Wire
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The dot product
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Dot vs. Cross Product
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Calculating dot and cross products with unit vector notation
Magnetism 9: Electric Motors Using a magnetic field to exert torque on a rotating circuit.
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- Let's say we have a magnetic field that's coming out of the
- right side of the screen.
- And it's not just along the screen, it's actually three
- dimensional.
- So it's going above the screen, below, but the
- direction of the magnetic field is from the
- right to the left.
- Let me just draw that.
- And I'm not going to draw a bunch of the field vector
- arrows because that'll just take up a lot of valuable
- space on our-- so that's the vector magnetic field.
- It's down here, too.
- If I could, I would draw it above your screen and below
- your screen.
- But it's coming from the right to the left.
- And then in that magnetic field I
- have an electric circuit.
- I won't draw the whole circuit right now.
- I'll do that in a second.
- But let's say I have-- part of the electric
- circuit is a loop.
- And the loop looks like this.
- I'm trying to draw it carefully.
- So that we can-- because I think a careful drawing will
- be more useful in a second than an
- uncarefully drawn drawing.
- So let's see.
- So it's a loop.
- You can almost-- you could imagine taking a paper clip
- and putting it into this shape.
- Oh, that's good enough, I think.
- And I have a current going in this direction
- in this paper clip.
- So this is the positive, that's the negative.
- So the current is going like that.
- Current is going in a loop like that.
- The current's coming out of this end, it's
- coming into this end.
- And let's say that loop of-- it could be a paper clip or
- anything-- let's say that it can rotate.
- And that's important.
- What's going to happen?
- Well, my magnetic field is coming in this direction.
- The current is going down here, up here.
- What's going to be the net force of the magnetic
- field on this loop?
- Well, let's try it out.
- And it turns out it's going to be a different magnitude at
- different points of the current.
- So here.
- And we don't worry about-- all we're worried about right now
- is direction.
- And then maybe a little intuition of the magnitude.
- So we know that the force of the magnetic field is equal to
- the current times the length vector cross
- the magnetic field.
- Well, what would be the force of the magnetic field on this
- segment of wire?
- We could call this L.
- And that L goes in the same direction as the current.
- Well, let's see.
- Current is just a scalar, but L is going down.
- Magnetic field going to the left.
- Cross product.
- Cross product, I take my right hand, put my index finger in
- the direction of the current, or in the direction of L,
- because that's the first term of the cross product.
- So that's the index finger.
- So my index finger goes down, because that's the direction
- of the current.
- And then my middle finger-- and remember, you have to do
- this with the right hand.
- If you do it with the left hand, you're going to get the
- opposite result.
- And now my middle finger is going to go in the direction
- of the field.
- So let me point my middle finger.
- My middle finger is going to go in the
- direction of the field.
- I keep having to look at my own hand.
- And then my other two fingers are just going to do what they
- need to do.
- So that's my third finger.
- That's my pinky.
- And then what is my thumb going to do?
- What is my thumb going to do?
- Well, my hand-- that's my hand.
- This is what my hand is doing.
- I'm pointing downward.
- And my palm is kind of pointing at my body.
- So what is my thumb doing?
- I know it's hard to see.
- This is my middle finger right here.
- So my thumb is on the other side of this drawing.
- And my thumb is pointing downwards.
- I hope you see that.
- And you try it with your own hand.
- So my thumb is pointing downwards.
- So the direction of the force created by the magnetic field
- on this current is going to go downward.
- So let me draw that.
- So the force vector-- I'll do it in this
- orangey brown color.
- The force vector on this segment of the wire is going
- to be going down.
- Now what about this segment of the wire?
- Well, think about it.
- This segment of the wire, the L vector-- this L vector--
- It's parallel to the magnetic field just in
- the opposite direction.
- And so when you take the cross product-- remember, the cross
- product is you're multiplying the magnitude of the vectors
- that are perpendicular to each other.
- But if this is the L vector right here, there's no
- component of it that it's perpendicular to
- the magnetic field.
- So the magnetic field and the current are in the same plane.
- They're parallel.
- They're not orthogonal at all.
- There's no components of them that are at 90 degrees.
- So when you take the cross product, you're going to see
- that the net force on this segment of the wire is 0.
- And likewise on this segment of the wire and this segment
- of the wire.
- Because they aren't in any way perpendicular.
- No components of them are even perpendicular.
- So fair enough.
- So all we know right now is the magnetic field is exerting
- a downward force on this side of our paper
- clip or of our circuit.
- Now what about this side?
- Well, same thing.
- Take the cross product.
- If this is our L, L cross B.
- So take your index finger in the direction--.
- So index finger goes like that.
- Your middle finger will go in the direction of the field.
- So your middle finger is going to look something like that.
- And then your other two fingers are
- going to be like that.
- And what is your thumb going to do?
- And this has to be your right hand to work.
- Your thumb is going to point straight up.
- This is like the heel of your thumb.
- Your thumb is going to--.
- I don't know if that's a good drawing of a thumb.
- But your thumb is essentially pointing out of the page.
- Middle finger in the direction of the current, or in the
- direction of our length.
- Sorry, index finger in the direction of the current.
- Middle finger in the direction of the field.
- Thumb points out of the page.
- Do that with your own right hand and you'll see that the
- net force of the magnetic field on this segment of the
- wire is going to be upwards.
- Let me do it in a different color just to get some
- contrast.
- So what's going to happen?
- Assuming that this circuit can rotate,
- what's going to happen?
- On this side there's a downward force.
- On this side there's an upward force.
- So the magnetic field is actually exerting a
- torque on this wire.
- If you viewed this little dotted line as our axis of
- rotation, the whole coil is actually going to rotate
- around that line.
- And so there's some force over here, along this whole line
- being applied downwards.
- And it's actually perpendicular
- to our moment arm.
- If you remember what we had learned about torque.
- So it will actually exert all of that force-- that force
- times this distance will be the torque
- applied on this side.
- And then likewise there's a torque-- it's really the same
- sign, in the same direction, because here on the other side
- of the arm it's pushing upwards.
- So they're not going to cancel out.
- They're both going to reinforce.
- And this whole coil is going to be
- turning in this direction.
- Here it's going to be moving up out of your video screen.
- Here it's going to be moving down into your video screen.
- Now what happens?
- I'm going to try to not run out of time either.
- So it's going to start rotating.
- So the left hand side's going to go below the page.
- The right hand side's going to be above the page.
- I want to draw some perspective, that's why I'm
- just drawing it bigger.
- Maybe it looks like that.
- Maybe my circuit starts to look like that.
- And I'll redraw my axis of rotation.
- So this is my axis of rotation.
- And on the way I drew it-- this part, the axis of
- rotation is still in the plane of our video.
- But this part of the coil is, you could
- imagine it popping out.
- I wish you had 3D glasses on.
- It's popping out of your screen.
- This part is going into your screen.
- And the current is still going in the same direction.
- Current is going in that direction there.
- So using the same right hand rule, on this side of the wire
- the magnetic field is going to be exerting a
- net downward force.
- But the torque is actually going to be less because our
- moment arm distance is going to be like-- I want to draw it
- with some perspective.
- It's going to look something like that.
- So it's going to be going to the left and behind the page
- while the torque is still just into the page.
- So you would actually take the component of the torque that's
- perpendicular.
- So there's some component of the torque that's actually
- perpendicular.
- I don't want to confuse you too much.
- But you could imagine the torque lessens.
- Even though the net magnetic force is the same, the
- component of that force that's perpendicular to your moment
- arm, that lessens.
- So there's still going to be some torque that's going to be
- causing it to rotate downwards in that direction.
- Sorry.
- You know what?
- I drew this wrong here.
- We're pushing up on the right hand side, we're pushing down
- on the left hand side.
- So the direction is going to be like that.
- Pushing up on the right hand, down on the left hand.
- So you're still going to be doing the same thing here.
- You are going to be pushing up here.
- But you're going to be pushing up directly out of the page.
- But that's not completely perpendicular
- to the moment arm.
- So the component that is perpendicular, that's actually
- creating rotational torque, that's going
- to be a little less.
- And then you could imagine that all the way to the point,
- the coil's going to keep rotating with smaller torque.
- At some point you'll be looking at it head on.
- So I can just draw it like a straight line, right?
- You can imagine.
- This arm is on top and this arm is behind it.
- And at this point, what's going to happen?
- All the magnetic force on this top arm is going
- to be popping up.
- It's going to be popping up out of your page but it's not
- going to be providing any torque.
- Because it's not perpendicular anymore to your moment arm.
- And likewise, on the bottom behind this, if you could
- visualize this, it would be exerting a net downward force.
- And that's also not going to be helpful.
- But maybe they have some angular momentum so the wire
- will still rotate.
- But then when it still rotates,
- what's going to happen?
- And this is where I'll leave you with a
- little bit of a conundrum.
- Actually, I don't want to go over the Youtube limit, so I'm
- going to continue this in the next video and I'll show you
- the conundrum.
- See you soon.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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