Question

A charge Q is placed at a distance a/2 above the centre of a horizontal, square surface of edge a as shown in the figure (30-E1). Find the flux of the electric field through the square surface.

Answer 1

Given:
Edge length of the square surface = a
Distance of the charge Q from the square surface = a/2
Area of the plane = a²

Assume that the given surface is one of the faces of the imaginary cube.

Then, the charge is found to be at the centre of the cube.

A charge is placed at a distance of about $\frac{a}{2}$ from the centre of the surface.
The electric field due to this charge is passing through the six surfaces of the cube.


Hence flux through each surface,

$\varphi =\frac{Q}{{\mathit{\in }}_{\mathit{0}}}\mathit{\times }\frac{1}{6}\mathit{=}\frac{Q}{\mathit{6}\mathit{}{\mathit{\in }}_{\mathit{0}}}$
Thus, the flux through the given surface is $\frac{Q}{6{\in }_0}$.