Question

A point charge $+Q$ is positioned at the centre of the base of a square pyramid as shown. The flux through one of the four identical upper faces of the pyramid is

• A. $\frac{Q}{8{\epsilon }_0}$
• B. None of these
• C. $\frac{Q}{4{\epsilon }_0}$
• D. $\frac{Q}{16{\epsilon }_0}$

Answer 1

The correct option is A $\frac{Q}{8{\epsilon }_0}$


Draw a similar pyramid in the upright position such that the charge $+Q$ lies at the centre of this new surface.
Gauss law: Flux through the surface is $Q/{\epsilon }_0$
Due to symmetry flux through the upper pyramid is $Q/\left(2{\epsilon }_0\right)$
This flux is equally divided into $4$ faces, so flux through any one surface is
$1/4(Q/2{\epsilon }_0=Q/8{\epsilon }_0)$