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
direction--.
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
interesting.
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
fingernails.
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.
See