$$\require{cancel}$$

# 1.6.6: Field of a Uniformly Charged Infinite Plane Sheet

All we have to do is to put $$α = π/2$$ in equation 1.6.10 to obtain

$E=\frac{\sigma}{2\epsilon_0}.\tag{1.6.12}$

This is independent of the distance of P from the infinite charged sheet. The electric field lines are uniform parallel lines extending to infinity.

Summary

\begin{align}&\text{Point charge Q :}\quad \quad \quad &&E=\frac{Q}{4\pi\epsilon_0 r^2}. \\ &\text{Hollow Spherical Shell: } &&E=\text{ zero inside the shell,} \\ & &&E=\frac{Q}{4\pi\epsilon_0 r^2}\text{ outside the shell} \\ &\text{Infinite charged rod :} &&E=\frac{\lambda}{2\pi\epsilon_0 r}. \\ &\text{Infinite plane sheet :} &&E=\frac{\sigma}{2\epsilon_0}. \end{align}