Magnetic fields question

Question

What happens if a DC motor or maybe even a generator, has a circular wire loop instead of a rectangular one?

Answer 1

It is not really the shape of the loop that matters, but the rate at which the magnetic flux is changing through the area encircled by the loop.  Suppose you have a circular area A and a rectangular area A, both rotating inside a uniform magnetic field B.  The magnetic flux is

 

Φ = BA cosθ,

 

where θ is the angle between the normal to the area and the magnetic field.  If the loops are rotating inside the field, then the only variable that matters here is the rate of change of θ, since the areas are the same.