All Problems

Constant Electric Field in a Vacuum

Problem 3.53

The field potential inside a charged ball depends only on the distance from its centre as φ=ar2+b,\varphi=a r^{2}+b, where aa and bb are constants. Find the space charge distribution ρ(r)\rho(r) inside the ball.

Reveal Answer
ρ=6ε0a\rho=-6 \varepsilon_{0} a