Question

A long string with a charge of $\lambda$ per unit length passes through an imaginary cube of edge $l$. The maximum possible flux of the electric field through the cube will be

• A. $\frac{\lambda l}{{ϵ}_0}$
• B. $\frac{\sqrt{2}\lambda l}{{ϵ}_0}$
• C. $\frac{6\lambda l^2}{{ϵ}_0}$
• D. $\frac{\sqrt{3}\lambda l}{{ϵ}_0}$

Answer 1

The correct option is D $\frac{\sqrt{3}\lambda l}{{ϵ}_0}$

Maximum length of string that can pass through cube is $=\sqrt{3}l$
Maximum enclosed charge $=\sqrt{3}l\lambda$
$\therefore \varphi =\frac{\sqrt{3}l\lambda }{{ϵ}_0}$