Finding E and B field of a weird charge distribution

[asdff529]

Homework Statement

Initially there is a spherical charge distribution of with a radius $R_0$ and uniform charge density $ρ_0$. Suppose the distribution expands spherically symmetrically such that its radius at time t is $R_0 + V t$, where V is the velocity. Assuming the density remain uniform inside the sphere as time increases, find the charge density and current density,E-field and B-field

Homework Equations

4 maxwell equations and continuity equation

The Attempt at a Solution

I have computed $ρ$ and $J$, so does E. I want to know if $J=ρV$ in r direction.Then I find that curl of E=0, which means B is independent of time, which is strange. And I find it very complicated to solve the Ampere's Law with Maxwell Correction.
Any hints? Thank you

 

[phyzguy]

Try reading this similar thread:

https://www.physicsforums.com/threads/magnetic-field-of-a-spherical-capacitor.739411/