Question

Two uniformly charged large plane sheets $S_1$ and $S_2$ having charge densities ${\sigma }_1$ and ${\sigma }_2({\sigma }_1>{\sigma }_2)$ are placed at a distance d parallel to each other. A charge $q_0$ is moved along a line of length a (a < d) at an angle ${45}^{\circ }$ with the normal to $S_1$.Calculate the work done by the electric field.

Answer 1

As we see $E_1=\frac{{\sigma }_1}{2{\epsilon }_0},E_2=\frac{{\sigma }_2}{2{\epsilon }_0}$

$E=E_1-E_2=\frac{{\sigma }_1-{\sigma }_2}{2{\epsilon }_0}$

$W=q_{0}E\times \frac{a}{\sqrt{2}}=\frac{q_{0}a}{2\sqrt{2}{\epsilon }_0}({\sigma }_1-{\sigma }_2)$