All Problems

Constant Electric Field in a Vacuum

Problem 3.51

The field potential in a certain region of space depends only on the xx coordinate as φ=ax3+b,\varphi=-a x^{3}+b, where aa and bb are constants. Find the distribution of the space charge ρ(x)\rho(x).

Reveal Answer
ρ=6ε0ax\rho=6 \varepsilon_{0} a x