Question

A charge $Q$ is placed at a perpendicular distance $\frac{a}{2}$ above the centre of the horizontal, square surface of edge length $a$ as shown in figure. Find the flux of the electric field through the square surface.

• A. $\frac{Q}{3{\epsilon }_0}$
• B. $\frac{Q}{2{\epsilon }_0}$
• C. $\frac{Q}{{\epsilon }_0}$
• D. $\frac{Q}{6{\epsilon }_0}$

Answer 1

The correct option is D $\frac{Q}{6{\epsilon }_0}$

Let us imagine a cube of edge $a$, enclosing the charge. The square surface is one of the six faces of this cube.

According to Gauss's law of electrosstatics, total electric flux $\left(\varphi \right)$ through the cube is given by

$\varphi =\frac{Q}{{\epsilon }_0}$

So we can also say that electric flux through six faces $\varphi =\frac{Q}{{\epsilon }_0}$

So the electric field flux through each face $=\frac{Q}{6{\epsilon }_0}$

Hence. option (b) is the correct answer.