Electric field intensity with a charge decreasing over time

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.


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