Question: A spherical ball of charge has radius R and total charge Q. The electric field strength inside the ball (r R) is E(r) =

A spherical ball of charge has radius R and total charge Q. The electric field strength inside the ball (r ≤ R) is E(r) = r⁴E_max/R⁴.
a. What is E_max in terms of Q and R?
b. Find an expression for the volume charge density ρ(r) inside the ball as a function of r.
c. Verify that your charge density gives the total charge Q when integrated over the volume of the ball.

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