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## Homework Statement

Consider a single coil that is turning in a constant and uniform magnetic field {\bf B} thanks to a motor. The normal to the coil is given by:

$${\bf u}(t)=\sin (\omega t){\bf u_x}+\cos(\omega t){\bf u_z}$$

How can we obtain the energy that the motor has to spend in a period [itex]T=\frac{2\pi}{\omega}[/itex]?

## Homework Equations

## The Attempt at a Solution

I haven't any good idea. I have thought that the energy given by the motor cold be trasformed in magnetic potential energy. Knowing that [itex]U_p=-{\bf m} \cdot {\bf B}[/itex] where [itex]{\bf m}=i \Sigma {\bf u_n}[/itex], [itex]U_{motor}=-U_p[/itex]. I could integrate it from 0 to T and I could obtain the energy spent by the motor during the time T. But I think that this procceding is wrong.

Many thanks for your help.