Question

Suppose the x − y plane is electrically charged with a constant charge density σ.
Find the electric field at a hight h from the x − y plane. Use Coulomb’s law.

Answer 1

Answer

Firstly understand planar symmetry

system only varies with distance from a plane.

For planar symmetry, a convenient Gaussian surface is a box penetrating the plane, with two faces parallel to the plane and the remainder perpendicular, resulting in Gauss’s law being $2AE=\frac{{q}_{\text{enc}}}{{\epsilon }_{0}}.$

$E=\frac{q}{2A\epsilon_0}=\frac{\sigma}{2 \epsilon_0}$