Question

Calculate the electric field at the centre of a non-conducting semicircular ring of linear charge density $\sigma$ as shown in the figure.

Answer 1

Net electric field $=\int 2dE\sin \theta =\int \frac{2kdq}{R^2}\sin \theta =\frac{2k\sigma }{R}\stackrel{\frac{k}{2}}{\underset{0}{\int }}\sin \theta d\theta$

$\because dq=\sigma Rd\theta$

$E_0=\frac{2k\sigma }{R}$