Electric field intensity with a charge decreasing over time

[ForTheGreater]

So a lossy dielectric sphere gets an initial charge distribution evenly across the sphere.

Find an expression for E inside and outside the sphere for all t.



I figured that σ∇E=dp/dt
p being volume denity.

So I apply spherical coordinates to the div of E and integrate over r to get an expression for E. But I need to do something with the dp/dt since I want t in the expression.

 

[BvU]

Hello For,

Perhaps you have a better chance to get some assistance if you formulate a bit more completely using the template. Lossy ? $\sigma$ <--> dp/dt ?