Moving a loop of wire away from a current carrying wire

[warfreak131]

Homework Statement

Hey all, I am studying for the GRE and I need help with this question:

A rectangular loop of wire with dimensions shown above (see attachment) is coplanar with a long wire carrying current I. The distance between the wire and the left side of the loop is r. The loop is pulled to the right as indicated.

What are the directions of the induced current in the loop and the magnetic forces on the left and the right sides of the loop as the loop is pulled?

Induced Current ... Force on Left Side ... Force on Right SideA. Counterclockwise ... To the left ... To the right

B. Counterclockwise ... To the left ... To the left

C. Counterclockwise ... To the right ... To the left

D. Clockwise ... To the right ... To the left

E. Clockwise ... To the left ... To the right

The Attempt at a Solution

Currently, the magnetic field from the current wire is moving into the page along the right side. As the loop is pulled away, it attempts to maintain the magnetic field. This means that the induced magnetic field along both sides of the loop are of the same orientation as before.

The left side of the loop experiences a greater magnetic force than the left side, meaning the current would travel clockwise.

If you look at the magnetic force, F=q(VxB), and calculate the force for a positive charge, the left side force would be to the left, and the right side force to the right. Since electrons are negative and travel in opposition to current, v becomes -v, and q becomes -q. This double negative cancels out, though.

 

[BruceW]

yep. You've got the right answer. I'm not sure what you mean by "the induced magnetic field along both sides of the loop are of the same orientation as before."

 

[warfreak131]

Thanks.

Take for instance if the loop was moving closer to the loop. It would want to maintain the original, weaker magnetic field. Therefore it would induce a magnetic field with the opposite polarity.

But since this is going away from the wire, it wants to maintain the original stronger field, so it induced a magnetic field with the same polarity.

 

[BruceW]

ah, yeah, that all sounds good. nice explanation.

 

[rwisz]

Therefore, the correct answer would be E. Clockwise ... To the left ... To the right. As the loop is pulled away, the magnetic field is maintained in the same direction, causing an induced current to flow in a clockwise direction. The force on the left side of the loop would be to the left, and the force on the right side would be to the right, as calculated using the right-hand rule for the direction of magnetic force on a current-carrying wire.