# Homework Help: Nonsinusoidal Induced EMF?

1. Jun 30, 2012

### Opus_723

1. The problem statement, all variables and given/known data

The book describes a rectangular loop of wire in a uniform magnetic field created by a pair of coils. It then discusses the emf that is produced when the rectangular loop rotates with constant angular velocity, noting that the induced emf varies sinusoidally with time.

At the end of the chapter, there is the following problem:

Does the prediction of a simple sinusoidal variation of electromotive force for the rotating loop depend on the loop being rectangular, on the magnetic field being uniform, or on both? Explain. Can you suggest an arrangement of rotating loop and stationary coils which will give a definitely nonsinusoidal emf? Sketch the voltage-time curve you would expect to see on the oscilloscope, with that arrangment.

3. The attempt at a solution

I'm pretty sure intuitively that so long as the loop lies in a plane, its shape does not matter. I am not sure whether a "bent" loop could possibly create a nonsinusoidal emf, but all my attempts at coming up with one that does so have failed. They all seem to end up with some variation of a sine wave. Granted, I could only visualize a few simple ones. I wish I knew some way to convince myself more generally, though. I think maybe you can join planar loops to make a nonplanar one, since the adjoining currents cancel out. Then you can add the flux contributions from all the loops. Since they all rotate at the same frequency, just out of phase, their sum has to give you a sinusoidal function (since any planar loop produces a sinusoidal emf). Maybe. I'm really fuzzy on that, and would like some input.

As for a nonuniform field, I just don't know. I'm stuck. I don't know if this problem is supposed to be more about visualization and intuition or if there's a straightforward way to answer it.

Last edited: Jun 30, 2012