Question

A linear charge having linear charge density $\lambda$, penetrates a cube diagonally and then it penetrates a sphere diametrically as shown. The ratio of flux coming out of the cube and the sphere is $\frac{\sqrt{x}}{y}$. Find $(xy)$.

Answer 1

Answer: 6

Flux coming out of the cube, ${\varphi }_1=\frac{\lambda \cdot a\sqrt{3}}{{\epsilon }_0}$...(i)
Flux coming out of the sphere, ${\varphi }_2=\frac{\lambda \cdot 2a}{{\epsilon }_0}$...(ii)
$\therefore \frac{{\varphi }_1}{{\varphi }_2}=\frac{\sqrt{3}}{2}$