Magnetic force on capacitor
I have this problem: I have a capacitor formed by two parallel square-shaped plates, of side , and with distance between them. They're asking me out of other things, the magnetic force as a function of some things. I calculate de magnetic force by calculating the gradient of the magnetic energy, given by:
I have calculated and , that form, during the charge of the capacitor, loops around the center proportional to , being the distance from the central axis. The problem is that I have to integrate that to a cubic volume: , one of those variables is independent, but the other two are not, and this problems never involve complicated integrals, such that one:
If the plates were circles it would be trivial, but being squares, I'm sure I'm missing something.