Question

The current I in a long, straight wire is constant and is directed toward the right as in Fig. E29.16. Conducting loops, A, B, C, and D are moving, in the directions shown, near the wire. (a) For each loop, is the direction of the induced current clockwise or counter clockwise, or is the induced current zero? (b) For each loop, what is the direction of the net force that the wire exerts on the loop? Give your reasoning for each answer.

Short answer

1. A: Counter-clockwise, B: Clockwise, C: Zero current and D: Counter-clockwise
2. A: Attracted, B: Attracted, C: No force and D: Repelled

Step-by-step solution

Find direction of current for all the loops

We need to determine the direction of the induced current in each one of the loops. The magnetic field due to a very long wire is inversely proportional to the distance from the wire, but as long we move beside the wire, the magnetic field stays constant. And as we go further from the wire the magnetic field becomes weaker. For loop A, it moves further from the wire so the magnetic field. So, according to Lenz’s law the induced current in the loop must flow such that to oppose the external magnetic field, to oppose the decrease in the magnetic field, the induced magnetic field must point out of the page, hence the induced current must flow counter-clockwise.

We have a similar case in loop B, but the magnetic field in the position of loop B is into the page, so the induced current must flow clockwise.

Loop C moves parallel to the wire, which means the magnetic flux through it is constant, so there is no induced current in this loop.

In loop D, the magnetic field increases as the loop moves towards the wire, to oppose this increase the induced magnetic field must be in the opposite direction of the magnetic field in the loop’s region, that is, out of the page. Hence, the induced current must flow counter clockwise.

Find the net force in each loop

In loop A, the flux is decreasing, so in order to increase the flux the loop is pulled toward the wire.

Similarly, in loop B the flux is decreasing, so in order to increase the flux, the loop is pulled toward the wire.

In loop C, no current is flowing, so there is no force acting on it.

In loop D, the flux is increasing, so in order to decrease the flux, the loop is repelled by the wire.