Finding E and B field of a weird charge distribution

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SUMMARY

The discussion focuses on a spherical charge distribution with a uniform charge density ρ₀ and a radius R₀ that expands over time as R₀ + Vt. The participant successfully computed the charge density ρ and current density J, questioning whether J equals ρV in the radial direction. They noted that the curl of the electric field E is zero, indicating that the magnetic field B is time-independent, which complicates the application of Ampere's Law with Maxwell's correction.

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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
 
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