Lorentz force -> Current in a gradient field

[Pogo]

This is doing my nut in. I'm looking at causes of errors in a rotating gradiometer. It uses a loop of superconductor formed so that the current in the loop is proportional to the gradient of the magnetic field threading the loop.

I think that an error current will arise due to the Lorentz force acting on the charges in the loop as it rotates in a field with a gradient. I'm approaching the problem by calculating the velocity of the electrons in each vertical arm of the loop, then summing.

To calculate the electron velocity, I have to integrate the acceleration due to the Lorentz force. When I integrate, I get two non-physical results. The first is a 1/omega term that cancels the omega term in the tangential velocity. That means that the current that was caused by the velocity persists when the velocity is zero. The second is a ramp term that arises from the integration. Electron velocity (current) is proportional to time which is again non-physical)

I'd be happy to provide diagrams and answer further questions, but I don't want to lead anyone down the same wrong path (if it is wrong) to get the same answers.

Would someone like to look at this with me?

Cheers;

Pogo.

 

[Pogo]

Further to this, I have been able to eliminate the second problem, the ramp, because the individual currents oppose, so one ramp cancels another. Now, if the velocity dependence would reappear...