Electricity and magnetism
Magnetism 10: Electric Motors Why the circuit will keep flipping over.
Magnetism 10: Electric Motors
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- Where I left off in the last video we saw that if we had a
- magnetic field coming in from the right and we had this loop
- of-- I guess we call it-- metal or a circuit, and it's
- carrying a current where the current is coming in this
- You can imagine positive protons, although we know the
- electrons go in the other direction.
- But the current is coming in this direction and going out
- that direction.
- We figured out using the right hand rule and just this
- formula, that the net force of the magnetic field coming in
- this direction on this arm of the wire or the
- circuit is net downwards.
- And on this arm, it was net upwards.
- And so it provided a net torque on this circuit.
- Or, as I said in the last video, a paper clip.
- And where this dotted line is the axis of rotation.
- And this is how I showed you it would rotate.
- Where the magnetic field is essentially pushing up on the
- right hand side and pushing down on the left hand side.
- It has no effect over here on the top and the bottom.
- So it would rotate in this direction.
- And then this was kind of what it looks like after it rotates
- a little bit.
- And the whole reason why I did this, I said, well, this arm--
- which is the same as this arm-- the net
- force is still upwards.
- Out of our screen.
- But that upwards direction is now no longer going to be
- completely perpendicular to the moment arm distance.
- That's the moment arm distance.
- Now the moment arm distance is kind of coming at an angle out
- of the page.
- So only some of this net outward force for the magnetic
- field is going to be perpendicular
- to the moment arm.
- And so the torque on it will be less, but it's still going
- to be torque in that same direction.
- Kind of coming out of the page on the right and into the page
- on the left.
- And the same is true of the left hand side.
- And you go all the way to the point that the coil is
- actually vertical.
- Where this side, this side right here, is on top.
- And this side is on bottom, below the plane
- of your video screen.
- And at that point, the torque-- actually, there is no
- net torque.
- And why is that?
- Because on this top part, when it's pointing straight out at
- you, when it's right here, the magnetic field-- the force of
- it, the force that's affecting the circuit-- is pushing
- straight up.
- So there's no longer any net torque because the force is
- pushing straight up and that moment arm distance-- this
- distance-- is now also pointing straight up.
- And torque is also a cross product, so you actually care
- about the perpendicular forces.
- So there, at this vertical point, there's no net torque.
- And the same is true at the bottom of the circuit.
- Because at the bottom the magnetic field force is going
- to be downwards, which is parallel with the moment arm
- distance, so there's no net torque.
- And I said, well maybe there's a little bit of angular
- momentum that keeps this object rotating.
- And then it will rotate to-- and this is where it gets
- I'll draw it neatly.
- Then it'll rotate to this point.
- Once again I want to have the perspective.
- It'll rotate here.
- So let me just make sure I have all of it.
- So here it was rotating in this
- direction and in that direction.
- And then here maybe some-- there's no longer any torque
- on it, but it still might on the top be moving to the left,
- and on the bottom moving to the right.
- Up to a point, then it's going to get into this configuration
- where soon. this side is-- so at this point it has rotated
- more than 90 degrees.
- So this edge is now this edge.
- It had rotated from here all the way-- it's still pointing
- out of the screen.
- But if this edge is the same as this edge, now the current
- direction is going to be like this.
- Because this edge has rotated down.
- So it's rotated from that position all the way back to
- this position.
- So the current is now coming-- let me make sure, let me draw
- that right.
- The current is coming like that, like that, like that.
- Going up here, to the right, up like that.
- So the current now on this left hand side, although it
- was the former right hand side.
- It's still going in that upwards direction.
- So when you take the cross product, what is going to be
- the net magnetic field on that?
- Or the force of the magnetic field?
- Well, you do the same right hand rule.
- Point your index finger up.
- Put your middle finger in the direction of
- the magnetic field.
- This is the palm, this is your other two fingers.
- Let me draw the fingernails, just so they're painted
- Not that mine are.
- Then your thumb points upwards.
- So on this side of the coil we still have an upwards force.
- And if you do the cross product, or you do the right
- hand rule on the bottom side, or the behind side, if you
- could imagine it, you're still going to have a
- net downward force.
- So now all of a sudden you could imagine--
- the thing had rotated.
- So it had rotated in the way I drew it here, where it pops
- out on this side and it goes in on that side.
- And it had done it all the way to the point where we had
- rotated more than 90 degrees, but now all of a sudden the
- net force through the magnetic field was going to reverse.
- Because the side that has a current going upwards is now
- the left hand side.
- So now the force from the magnetic field is out on this
- side and you're going to want to rotate in
- the opposite direction.
- Hopefully that makes sense.
- Just think about what happens.
- Visualize this coil rotating.
- So what is essentially going to happen is you're going to
- rotate like I did here on the top.
- Maybe once you get to this level you're going to have a
- little bit of angular momentum that'll keep you rotating.
- Or rotational inertia that'll keep you rotating until you're
- in something like this configuration.
- Maybe you go all the way back to this configuration, where
- it's essentially a complete 180 degree turn.
- And then since on this side the current's going to be
- going up and on this side the current's going down, because
- you've essentially flipped this thing over, then the
- effect of the magnetic field is going to say, well, upwards
- on the left, downwards on the right.
- And so it's going to turn the other way.
- So if you think about it, it's going to keep oscillating.
- Let me draw it from-- well, I don't want to draw it from
- that angle, because I don't want to confuse you.
- So we have a problem.
- If we wanted to turn this into some type of electric motor
- and keep it spinning, we would either have to reverse the
- current once you get into this configuration, or either turn
- off the magnetic field.
- Or maybe you could reverse the magnetic field to get it going
- in the other direction.
- And actually you have another problem, which is a slightly
- lesser problem, is if this was a circuit and you just kept
- turning over and over the circuit, the wires would get
- twisted here.
- So you couldn't do it indefinitely.
- So the solution here is something called a commutator.
- you So let me draw a commutator.
- I have the same circuit which I've now drawn messier.
- But it has these two leads.
- It has these leads that essentially curve.
- You could imagine them curving out of the page.
- And then we have a circuit.
- You could imagine leads here, too.
- And this round thing and this thing are touching each other
- the whole time, so current could pass through it.
- Let me draw my battery.
- This is positive and this is negative.
- So up here on the circuit the current's always going to be
- flowing in this direction.
- It's always going to be flowing in this direction,
- it's always going to be flowing up and like this.
- Now when you're in this configuration,
- what's going to happen?
- Well, the current is going to flow down here.
- That's going to be I and that's going to be I.
- And when you do your right hand rule, we have the same
- magnetic field.
- I haven't changed the magnetic field coming in from the left.
- So just like we did before I cleared the screen, you use
- the right hand rule and you'll figure out, well, the net
- force from the magnetic field is going to be upwards here
- and downwards here.
- And that's what's going to create that net torque.
- And you're going to rotate this part.
- So this part of this
- contraption is going to rotate.
- You could imagine maybe there's like
- a little pole here.
- Maybe it's a nonconducting pole so that none of the-- and
- it's connected to an axle somewhere.
- So you can rotate along that axis, right?
- So the force of the magnetic field is
- going to create a torque.
- We're going to rotate up on this side, up out of the page
- on that side, and into the page on that side.
- And then behind the page and then back out of the page.
- That's what the net torque would be.
- And then we would get it, and it would keep doing that until
- you get to the vertical configuration.
- So at the vertical configuration, the circuit on
- the top stays exactly the same.
- I'm trying my best to draw this properly.
- At the vertical configuration one of two things can happen,
- and probably the best thing is that we actually lose contact
- with the two leads.
- So maybe the actual current stops flowing when we're in
- the vertical configuration.
- I'll do it in the same color.
- So when we're vertical we just see the top.
- We see this.
- And then we see it pops out a little bit.
- And then we see this arm right there.
- And then we see that pole that's maybe holding it or
- that's helping it rotate.
- But we're still having some-- you know,
- the current has ceased.
- So there's not going to be any torque, no force through the
- magnetic field, because we've lost touch at that point.
- Because these things kind of point out.
- Hopefully you could visualize how to build such a thing.
- And we're still rotating in this direction because of some
- type of rotational inertia.
- Then this is what the interesting part is.
- What happens when we rotate more than 90 degrees?
- And I just realized that I'm pushing over 10 minutes, so
- you can think about that a little bit while I stop here
- and continue this in the next video.
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