Modelling eddy currents in a pendulum

[FabusMarco]

Hello,
I was solving a problem related to Eddie currents recently and I need some help with simulating it numerically. Basically, we have a disc-like copper pendulum entering a region of uniform magnetic flux density B (see diagram). I understand that I need to use Faraday's law:
$$\nabla \times \vec{E} = - \frac {\partial{\vec B}} {\partial t},$$
but even if I assume B is in the z-direction and E is in the x-y plane, I am left with
$$\frac {\partial{E_y}} {\partial x} - \frac {\partial{E_x}} {\partial y} = - \frac {\partial{B}} {\partial t}.$$
Once I have E, I can find J and subsequently the current induced. However, do I not have too many variables? And how could I then find the retarding force, given that it depends on things like the velocity of moving charges?

Many thanks for your help in advance.

Diagram:

 

[kuruman]

If I were attacking this problem, I would not use a top-down approach. Instead of a disk, I would start with a circular loop; once I understand the loop, I can integrate loops to get the disk. Also, I would first consider the loop going into the field region in a straight line; once I understand that, I can extend to the arc of a pendulum.

 

[FabusMarco]

If I were attacking this problem, I would not use a top-down approach. Instead of a disk, I would start with a circular loop; once I understand the loop, I can integrate loops to get the disk. Also, I would first consider the loop going into the field region in a straight line; once I understand that, I can extend to the arc of a pendulum.

Thanks for the idea, I'll try it out!