Loop moving through a magnetic field

[sona1177]

Homework Statement

A square metal loop made of four rods of length L moves at constant velocity. The magnetic field in the central region has magnitude B; elsewhere the magnetic field is zero. The loop has resistance R. At each position 1-5, state the direction (CW or CCW) and magnitude of current in the loop.

a is the left rod, b is the top rod, c is the right rod, d is the bottom rod. THe loop moves to the right. At position 1, it is not in the magnetic field. At position 2, there is motional emf in side c only. IN position 3, there are motional emfs in both sides a and c.

Homework Equations

For the direction of the current in side c, I know it can either point in the top direction or the bottom. So I curl my fingers in the direction of the magnetic field in the interior of the loop, which is into the page, doesn't this mean my thumb points in the direction of the current, which is down, and hence clockwise? I don't understand why for part c, my book says counterclockwise. someone please help!

The Attempt at a Solution

 

[Doc Al]

For the direction of the current in side c, I know it can either point in the top direction or the bottom. So I curl my fingers in the direction of the magnetic field in the interior of the loop, which is into the page, doesn't this mean my thumb points in the direction of the current, which is down, and hence clockwise? I don't understand why for part c, my book says counterclockwise. someone please help!

The induced current opposes the change in magnetic flux. (That's Faraday's law.)

Alternatively, consider that the wire is moving to the right, so what force do the charges in the wire experience due to the magnetic field?

 

[sona1177]

Doc Al,

Yes, in the problem the loop moves to the right. But I want to try to solve it using the right hand rule where you point the thumb of the right hand in the direction of the current. Curl fingers inward toward palm, direction that fingers curl is direction of magnetic field lines around wire. So in this case, the current can either point up or down. When the current points down, the magnetic field points into the page, and so the current moves in the clockwise direction.

Alternatively, i can use F= qv x B. So the velocity is to the right, B is into the page, magnetic force on a positive charge would point up, current points up (counterclockwise direction). I want to know why I am getting two different directions for the current using two different right hand rules and this is really bothering me because I have an exam soon and don't want to end up in this situation. Can you tell me why I am getting two different directions.

 

[Doc Al]

Can you tell me why I am getting two different directions.

Yes. When you applied the right hand rule in the first case you forgot that the induced current opposes the change in flux. (You found the current that would create the flux, not the current that would oppose the flux.)

 

[sona1177]

Yes. When you applied the right hand rule in the first case you forgot that the induced current opposes the change in flux. (You found the current that would create the flux, not the current that would oppose the flux.)

So does the first case not apply when the magnetic field is changing (well the magnetic field isn't changing the portion of area submersed in it is)? This question comes before the section in my text regarding Lenz's law so I am not familiar with that yet.

 

[Doc Al]

So does the first case not apply when the magnetic field is changing (well the magnetic field isn't changing the portion of area submersed in it is)? This question comes before the section in my text regarding Lenz's law so I am not familiar with that yet.

You need to understand the minus sign in Faraday's law (which is Lenz's law) in order to find the induced current using that method.

 

[sona1177]

You need to understand the minus sign in Faraday's law (which is Lenz's law) in order to find the induced current using that method.

Now I understand what you are saying, however in position three, when there are motional emf's in sides a and c, does the current in side "a" point down? Because the flux is increasing, so the magnetic field in the interior of the loop has to point outward, to do this, my thumb has to point down in side "a".

 

[Doc Al]

Now I understand what you are saying, however in position three, when there are motional emf's in sides a and c, does the current in side "a" point down? Because the flux is increasing, so the magnetic field in the interior of the loop has to point outward, to do this, my thumb has to point down in side "a".

Once both a and c are both within the field, there's no change in flux so there's no current. (Assuming I understand the situation properly.) The motional EMFs on each side point in the same direction, thus cancel.

(Remember that it's the change in flux that counts, not just the flux.)

 

[sona1177]

Once both a and c are both within the field, there's no change in flux so there's no current. (Assuming I understand the situation properly.) The motional EMFs on each side point in the same direction, thus cancel.

(Remember that it's the change in flux that counts, not just the flux.)

Well my book explains it this way: the current in side a points up and the current in side c points up also. But I don't understand how the current in side a points up. Is the magnetic flux decreasing there?

 

[Doc Al]

Well my book explains it this way: the current in side a points up and the current in side c points up also. But I don't understand how the current in side a points up. Is the magnetic flux decreasing there?

Think of it in terms of motional EMF. Both side a and side c are moving in the same direction through the magnetic field, so the EMF they would feel points in the same direction.

As I said before, the magnetic flux through the loop is not changing at that point in the motion, so the net EMF and current is zero.