All Problems

Constant Electric Field in a Vacuum

Problem 3.38

A charge \(q\) is uniformly distributed over the volume of a sphere of radius \(R\). Assuming the permittivity to be equal to unity throughout, find the potential (a) at the centre of the sphere; (b) inside the sphere as a function of the distance \(r\) from its centre.

Reveal Answer
 (a) φ0=3q8πε0R (b) φ=φ0(1−r23R2),r⩽R\text { (a) } \varphi_{0}=\frac{3 q}{8 \pi \varepsilon_{0} R} \text { (b) } \varphi=\varphi_{0}\left(1-\frac{r^{2}}{3 R^{2}}\right), r \leqslant R
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