Question

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

• A. $\frac{1}{2}$
• B. $\frac{2}{\sqrt{3}}$
• C. $\frac{\sqrt{3}}{2}$
• D. $\frac{1}{1}$

Answer 1

Answer: (C)

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