Answer to Question #107209 in Electricity and Magnetism for Anas Nayfeh

Question

Charge of a uniform density 8 nC/m^2 is distributed over the entire xy plane. A charge of uniform density 5nC/m^2 is distributed over the parallel plane defined by z=2m. Determine the magnitude of the electric field for any point with z=1

Answer 1

The electric field due to the charged plane is uniform

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

The superposition principle says

$$E_{net}=E_1-E_2=\frac{\sigma_1}{2\epsilon_0}-\frac{\sigma_2}{2\epsilon_0}$$ $$=\frac{8\times 10^{-9}}{2\times 8.85\times 10^{-12}}-\frac{5\times 10^{-9}}{2\times 8.85\times 10^{-12}}=170\:\rm V/m.$$