Suppose a solid metal plate moves trough a homogenous magnetic field $\vec{B}$ as shown in the following image. You will see that the plate will slow down (as long as not the entire plate is in the homogeneous field).
For example in the upper part of the plate in the picture there are eddy-currents induced because the magnetic field is changing in that region (the part of the plate is going to enter the homogenous magnetic field).
To explain that the plate is slowed down often Lenz law is cited which states in this case that the magnetic field produced by the eddy-currents is opposes the changing magnetic field.
But how can one explain that this leads to a force which slows down the plate in detail? In particular the situation is not so easy such that one could speak of magnetic north and south poles...
Is there a general mathematical expression for the force in this case?
(It's clear that one cannot calculate it already because I didn't give any technical details, but I just want a general equation for this situation which illustrates the concepts in this example from a mathematical point of view)
Do you have any good references about this point?