Magnetic vector potential and electric field in an oscillating cylinder

[michaelsagi]

Homework Statement

An infinite 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)

One asks:

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

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 !

 

[Eynstone]

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