Bar magnet at constant velocity, what is the direction of the induced current?

[imatreyu]

Homework Statement

A bar magnet is spun at constant angular speed w around an axis as shown in Figure P31.38. A stationary flat rectangular conducting loop surrounds the magnet, and at t = 0, the magnet is oriented as shown. Make a qualitative graph of the induced current in the loop as a function of time, plotting counterclockwise currents as positive and clockwise currents as negative.

Homework Equations

The Attempt at a Solution

I don't even know how to start this.
Of course, Lenz's law is relevant. . .Do I have to use the right hand rule to determine the direction of the currents?

I'm pretty sure that the graph ultimately resembles a sin graph, but I don't understand why.

Thank you, in advance )))

 

[anathema]

Dear forum post author,

Thank you for your question. Yes, Lenz's law is indeed relevant in this scenario. To determine the direction of the induced currents, you can use the right hand rule. As the magnet is spun at a constant angular speed, the magnetic field passing through the loop will also change at a constant rate. According to Faraday's law, this change in magnetic field will induce an EMF (electromotive force) in the loop, which in turn will cause the induced currents to flow in the loop.

Since the magnet is initially oriented as shown in the figure, the magnetic field passing through the loop will increase as the magnet spins counterclockwise. This will induce a counterclockwise current in the loop, as per Lenz's law. As the magnet continues to spin, the magnetic field passing through the loop will decrease, causing the induced current to decrease and eventually change direction. This will result in a negative (clockwise) current in the loop.

As the magnet completes one full rotation, the induced current will complete one full cycle, resulting in a graph that resembles a sine wave. This is because the magnetic field passing through the loop is changing at a constant rate, resulting in a sinusoidal variation of the induced current. The amplitude of the graph will depend on the strength of the magnetic field and the size of the loop.

I hope this helps you understand the concept better. If you have any further questions, please do not hesitate to ask. Good luck with your studies!
Scientist