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...

 

[astrokreng]

I can understand your frustration with this problem. The Lorentz force is a fundamental concept in electromagnetism and it plays a crucial role in understanding the behavior of charged particles in a magnetic field. In this case, it seems like you are trying to understand the effect of a gradient magnetic field on a loop of superconductor, and how it can cause errors in a rotating gradiometer.

It is important to note that the Lorentz force is the force exerted on a charged particle moving in a magnetic field. In this case, the charged particles are the electrons in the superconductor loop. As the loop rotates in a gradient magnetic field, the electrons experience a varying magnetic field, which causes them to move in a circular motion due to the Lorentz force. This results in a current in the loop, which is proportional to the gradient of the magnetic field.

Now, to address the errors in your calculations, it is important to consider the full equation of motion for the electrons in the loop, taking into account not just the Lorentz force, but also the effects of the superconductor material and any external forces. Additionally, the integration of the acceleration should result in a change in velocity, not a ramp term. It is possible that there may be other factors at play in your calculations that are leading to these non-physical results.

I would suggest consulting with a colleague or seeking guidance from a mentor or expert in this field to help you troubleshoot and refine your calculations. It is always helpful to have a fresh perspective and someone to bounce ideas off of. I also recommend double-checking your equations and assumptions to make sure they are accurate.

I hope this helps and I wish you all the best in your research.