Question

A charge $Q$, far from other charges, is fixed a distance $\frac{1}{2}s$ above the center of a square with side length s as shown in the diagram. What is the value of the electric flux that passes through the square due to the charge $Q$?

• A. $\frac{Q}{{ϵ}_0}$
• B. $\frac{Q}{2{ϵ}_0}$
• C. $\frac{Q}{3{ϵ}_0}$
• D. $\frac{Q}{4{ϵ}_0}$
• E. $\frac{Q}{6{ϵ}_0}$

Answer 1

Answer: (E)

$\frac{Q}{6{ϵ}_0}$

Let the Gaussian cube of side $s$ such that the charge is placed at its centre.

Thus electric flux passing through the cube ${\varphi }_{cube}=\frac{Q}{{ϵ}_o}$

As the charge is placed symmetric about all the 6 faces of cube, thus flux passing through one face is equal to the one-sixth of the total flux passing through the entire cube.

$\therefore$ Flux passing through the square ${\varphi }_1=\frac{{\varphi }_{cube}}{6}=\frac{Q}{6{ϵ}_o}$