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## Physics library

# Electric motors (part 3)

Sal finishes the explanation of how a commutator will allow a loop of wire to continue spinning in a magnetic field, thereby allowing it to work as an electric motor. Created by Sal Khan.

## Want to join the conversation?

- in the generator the coil is moved,this induces current in it.on the other hand this current may also be responsible for generating a force on the coil.according to me , one situation will use right hand rule another the will use left hand rule.

if the magnetic field and current remains constant the the direction of force will be opposite in the two cases.is this the effect of the lenz's law which states that the induced current opposes the cause that produces it(10 votes) - Aren't the rotational arrows supposed to be going in the opposite direction? Sal corrected himself in the first Electric motor video but he forgot to do it here.(8 votes)
- I have the same question. I think you're right!!(5 votes)

- When the resulting electromagnetic force isn't exactly in the direction of the circular motion (ie when the circuits's lower part isn't at a perfect 90゜ angle relative to the force), part of the force is pressing the side-circuits away from the center of rotation, right? Am I correct in assuming that because of this, even if you do use a commutator the magnetic field can't be too strong because then it would deform the circuits?

If that's not the case, please explain why! Thank you.(8 votes)- well, I think if you want to give the thing a good amount of torque, you put a heavy object in the middle and wrap the wire around that (for better momentum). The heavy object would also help resist against the deformation you speak of.

However, your reasoning is sound(3 votes)

- can any one tell me hoe to measure magnetic flux??

basically wats a proper definition and explanation of magnetic fulx..??

thnk u(2 votes)- Richard is right. The units are Webers. 1 Weber= 1 Tesla times 1 square meter. It tells you how much of a magnetic field passes
**directly**through a surface (i.e. what component is perpendicular). Conceptually, this isn't difficult, but it changes how we calculate magnetic flux. Instead of just taking the product of area and field strength, we need to take the product of area and the component of field strength normal to that area. For this we use the dot product. Here are some ways of finding magnetic flux mathematically (in decreasing difficulty).

If you have been through a multivariable calculus class then you know how to take the surface integral. Magnetic flux is defined mathematically as the surface integral of the dot product between the magnetic field vector and the differential area vector, over the whole surface. In physics and calculus the area vector has a direction normal to the surface (which means it points straight out). It looks like this (\Phi)=int(B dot dA). The math can get tricky, but this definition will work no matter how ugly your problem looks.

Another way, which is what you see in most examples, assumes a uniform magnetic field, and flat surface. If this is true, then you can pull the magnetic field vector outside of the integral as a constant. Then you have (\Phi)=B dot int(dA). The integral of dA is then just A (the area vector), and (\Phi)=B dot A. If you do not know the dot product, this is equivalent to (\Phi)=B*A*cos(/theta), where we treat B and A as scalars (values without direction), and /theta is the angle between the direction normal to the area and direction of the magnetic field. This is the first formula I learned for magnetic flux, and I always found it easy to remember because the equation looks like "Oh: BAcon"(7 votes)

- i knw this could be silly but when you are using the right hand rule for the right hand side of the circuit, do u have to invert your hand?(2 votes)
- Sometimes you do. I was in the U.S. Navy nuclear field and had to learn motor and generator theory. It was funny looking around during exams and seeing people contorting their hands to figure out the correct directions using the right-hand rules.(6 votes)

- Why is the rotation counter-clockwise. If the force on the left is acting into the screen, and the force on the right is acting out of the screen, shouldn't it be rotating clock-wise? I mean, in the previous video, it was rotating clockwise.(3 votes)
- The last video had 2 problems. The last one is diagrammed to start this video. Rewatch the last video at9:02to see where he demonstrates that it rotates counterclockwise.(2 votes)

- I'm a little confused. Does the commutator switch the direction of the current? If so, does it make the DC motor a AC motor?(2 votes)
- It does switch the direction of the current but it stays a DC motor(2 votes)

- Can I get to know what a Cyclotron is, how does it works and what it does?(2 votes)
- A cyclotron is a way to accelerate particles with a strong static magnetic field and a changing electric field

It goes like this:

The cyclotron is composed of two semicircles(a and b) with a distance d separating both of them, and there's an electric field between them that imposes a potential difference of V. The proton starts at a's surface facing b, with a potential V and its accelerated by the electric field until b, gaining a kinetic energy of V.q

When it gets to B, the magnetic field of intensity B takes over and the proton realizes a circular motion of radius r

magnetic force F = q.v.B = mv²/r , r = mv/Bq

Since mv²/2 = Vq , then v = sqrt(2Vq/m) , so r = m.sqrt(2Vq/m)/Bq = sqrt(2Vm/q)/B

So, r = sqrt(2Vm/q)/B , and the time it takes for the proton to come to b until it realizes half of a circle and reaches b again is f = pi.r/v = pi.m/Bq

Now, when the proton reaches b, the electric field must have changed (it needs to be set up to do so), in such a way that now b is at a potential V and a at a potential 0. This way, the proton, once again, gains a kinetic energy Vq from the electric field. Only this time, the radius increased, according to the equation written above

r = mv/Bq , where v is, now, sqrt(4Vq/m)

The ratio r/v, however, remains constant and equals to m/Bq , so f is constant and always equal to pi.m/Bq

So, the electric field must be always changing at this rate, in order for the proton to keep drawing semicircles with a growing radius and speed. At some point, the particles may get so fast you need to account for relativistic effects, too.(2 votes)

- I still dont understand the difference between AC and DC motor(2 votes)
- The main difference in AC and DC motors is that they are based on different types of current. Because of this the design of the motors has to be different. For DC motors the design has to change how the current is applied to motor since DC current doesn't change where as with AC current you can leverage the changing current to operate the motor.(2 votes)

- I don't get how the commutator solves the problem of the wires twisting I get that it reverses the current so that it can keep the torques steady but how does it untwist the wires then?(2 votes)
- The wires in the diagram are free floating. The wires he was originally talking about were those connected to the battery.(2 votes)

## Video transcript

So where I had left off
is we had the circuit. We had these little
leads here. This was kind of
our innovation. And this is actually called a
commutator, where this part that's connected to our rotating
piece, that's the commutator. And these are the brushes. So you could imagine, you could
design them as brushes that always stay in touch. Kind of like the brushes
on a, what was that? What are those cars at
the amusement park? Bumper cars, right? On the bumper cars you have a
pole behind your bumper car. I'll draw that for fun. So let's say this is
your bumper car. Looks like a shoe
a little bit. This is you driving
your bumper car. And they have a pole. And at the top of the pole,
you'll see these brushes that are touching the
ceiling, right? You could view that as the
same type of brush. And what it allows is a constant
electric current to flow through the ceiling. I don't know what direction
it's going in. But it allows a current to
flow through the ceiling. And maybe your car is grounded
so the current can flow down to ground, so that your car
could be powered by the ceiling and not have to carry
a battery in every car. Which would be kind of a waste
of energy and probably some type of a health hazard
and safety risk, et cetera, et cetera. So those brushes on your bumper
cars might not be all that different from the brushes
that are touching the commutators here. Just a little bit
of terminology. And it never hurts to
introduce bumper car references. I probably should have done
them earlier when we were learning about momentum
and things. But anyway. So what was happening here? So going back to our
first video. We have the current going
down like this. And then if you use your right
hand rule with the cross product, you know that the net
force from the magnetic field is going to be downwards on the
left hand side, upward on the right hand side. So you have a net torque
rotating it like that. Rotating the right out of the
page, the left into the page or into the video screen. Up to the point that you've
rotated 90 degrees and now you're looking kind of, so
this side right here. Let me do it in a different
color so you can see it. This side is this side,
right on top. And this side is on the bottom,
below the page. This side is now
above the page. If this distance is r,
this side is now r units above the page. And I said ideally maybe your
commutator loses touch with the brushes at this
point, right? Because they're popping out a
little bit, so when you're vertical, you actually lose
touch with the brushes. So you have no circuit flowing,
so you save a little battery energy. And you just let a little bit of
the angular momentum carry this whole rotating contraption
further a little bit to the point that
your configuration will look like this. So I know I keep changing
colors, but the whole contraption will now
look like this. OK, that's my positive,
negative, positive, negative, current flows like this. Now we assume that the
commutator has gotten back in touch. And let me color code this. So if this side is this
color, right? Now this is when we're looking
at top on, where it's popping out of the screen, where
it's above the screen. And now we've rotated 180
degrees and this side is on this side, right? Let me pick a suitable color. If this side was green. Now this side, we flip the whole
thing over 180 degrees. And now something interesting
happens. Remember, before we had this
commutator and everything, if we just flipped it over, the
current, because before when we didn't have the commutator,
the current here was flowing down here, up here. And before the commutator, we
had the current flowing down here and up here. And so we were switching
directions. And so you would have had this
thing that would never completely rotate. It would just keep flipping
over, right? Which may be useful for, I don't
know, if you wanted to flip things. But it's not useful
as a motor. So what happens here? Now this side, all of a sudden
instead of being connected to this lead, is now connected
to this lead. And this green side is now
connected to this lead. So something interesting
happens. Now the current on the left side
is still flowing down, right, and the current
on the right side is still flowing up. So we're back to this
configuration except that this contraption has flipped over. The brown side is now on the
left and the green side is now on the right. And what that allows is that
those net torques are still going in that same rotational
direction. Use your right hand rule. The current is flowing
down here. So if your magnetic field is
coming to the left, then the net force is going to be
down there and it's going to be up there. And so we can continue
indefinite, and we solve our other problem. That we will never keep twisting
these wires here. So now using the commutator, we
have essentially created an electric motor. And remember I drew that little
thing, that could be like the axle. Maybe that turns the wheels
or something. So if you have a constant
magnetic field and you just by using this commutator which,
as soon as you get to that kind of vertical point, it cuts
the current, and then when you go a little bit past
vertical, a little bit past 90 degrees, it switches the
direction of the current. So on the left hand side you
always have the current coming down, and on the right hand
side you always have the current going up. So that the net torque is always
going to be pushing, is always going to be rotating this
contraption down on the left hand side and up on
the right hand side. Coming out of the page on the
right hand side and then down on the left hand side. And you could actually
turn a wheel now. You could create an
electric car. So that is the basics
really of how electric motors are created. Well, there's another way
you could have done it. You didn't have to use
the commutator. One methodology you could have
used is you could have had the magnetic field going until you
get to this point, and then you turn off the magnetic
field, right? And maybe you wait for this
situation to go all the way 180 degrees and then you turn
the magnetic field back on again, right? That's one possibility. But that's maybe not as
efficient cause half of the cycle you're not powering it. Or maybe you switch
the direction of the magnetic field. Or another option, you don't
have to use a commutator. Maybe you use some other
contraption to switch the direction of the
magnetic field. But this is probably the
simplest way to do it. And I think it gives you a
general idea of how an electric motor can be created. And then we could play around
with the mechanics of innovations on it. But all electric motors are
essentially some variation of what you have learned
in this video. Isn't it neat to learn
something useful? See you in the next video.