# Lorentz force

1. Jun 22, 2010

### Gavroy

Hey,
I asked myself, how can I use:
$$U=\oint (v\times B) ds$$(1)
to calculate for example the alternating voltage of a conductor loop turning in a constant magnetic field. But I am not only interested in this case, I just want to illustrate it.
Therefore I thought about using Stokes theorem:
$$U=\int rot(v\times B) dA$$(2)
But I do not know how to deal with $$rot(v\times B)$$ in this equation.
How could I for exmple derive the equation of the alternating voltage
by using either equation 1 or 2.

Sorry about my english, but I do not live in an english-speaking country;-)

2. Jun 29, 2010

### AJ Bentley

The emf produced in the loop at any given moment is simply that produced by the movement of the coil through whatever field it is experiencing at that time.

So all you need to do is to work out the emf produced at each point in the rotation by the tangential velocity through the field at whatever angle it is currently at. (Think about it in terms of rotating the magnet around the wire instead of vice-versa).