Electromagnetic - finding the complete field by knowing either E or B

[sixers0130]

Homework Statement

B field = xt in z direction in Cartesian Coordinate, t is time.

Homework Equations

obtaining the remaining field expression together with charge densty "rho" and conduction current J, so that all Maxwell's equations are satisfied. There is no unique solution.

The Attempt at a Solution

I tried to apply Ampere's law on the given B field, but the right side will have two unknown variables to solve (J and dE/dt). I know E filed will only have y component by taking curl of B, so I try to do it backward on Faraday's law... and I'm stucked. Can someone give me a basic method to approach?

 

[sixers0130]

forgot to mention all quantities are vectors here