Question

A linear charge having linear charge density $\lambda$, penetrates a cube diagonally and it penetrates a sphere diametrically as shown below. What will be the ratio of flux coming out of the cube and the sphere?

Answer 1

Charge enclosed in cube = $\lambda \times Diagonal$

$=\lambda \times \sqrt{3}a$
Charge enclosed in sphere = $=\lambda \times Diameter$
$=\lambda \times 2a$
$\therefore \frac{{\varphi }_{cube}}{{\varphi }_{sphere}}=\frac{\frac{q_{cube}}{{ϵ}_0}}{\frac{q_{sphere}}{{ϵ}_0}}=\frac{\sqrt{3}}{2}$