Question

A pyramid has a square base of side $a$, and four faces which are equilateral triangles. A charge $Q$ is placed on the centre of the base of the pyramid. What is the net flux of electric field emerging from one of the triangular faces of the pyramid?

• A. $0$
• B. $\frac{Q}{8{ϵ}_0}$
• C. $\frac{Q{a}^2}{8{ϵ}_0}$
• D. $\frac{Q}{2{ϵ}_0}$

Answer 1

The correct option is B $\frac{Q}{8{ϵ}_0}$

Side $=a$

Charge $=Q$

The reasoning is that, as the problem is given, the charge in within as asymmetrical volume because the triangles faces have a different area than the square base. By adding another pyramid a symmetrical octahedron is formed and since the charge was the center of the base it is now at the center of the octahedron.

The total flux $\frac{Q}{E_0}$ is due to the flux through each face so each of the faces must be at $\frac{1}{8}$th of the total flux. The means that its distance from each of the triangular face is equal and, therefore the flux through each face is the same.

Hence Net electric flux $=\frac{Q}{8E_0}$