# A question from my EMF exam

1. Jul 15, 2010

### michaelsagi

1. The problem statement, all variables and given/known data

An infinte cylinder (radius a) with a uniform volume charge density rho_v is given. The axis of the cylinder coincides with the z axis. The following magnetic field exists:

B=B0cos(wt+a) for r<=a (i.e., inside the cylinder and on its walls)
B=0 for r>a (i.e., outside the cylinder)

1) What is the magnetic vector potential everywhere
2) What is the electric field everywhere
3) What can one learn from the magnetic field boundary conditions

3. The attempt at a solution

Unfortunately, I do not have any clue how to address this question. There is a static charge which generated a static electric field, and there is an induced electric field due to the alternating magnetic field. Is the overall electric field a superposition of the two electric fields or am I mistaken ? Do the boundary conditions imply that the cylinder behaves as an ideal solenoid ? Do I only need to find the rotor of the magnetic field to get the magnetic vector potential ?

Thank you for the help !!!

Last edited: Jul 15, 2010
2. Jul 16, 2010

### Eynstone

It's straightforth once you use Maxwell's equations (with vector potential).