Question

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

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

Answer 1

The correct option is D $\sqrt{3}\lambda a/{ϵ}_0$

The maximum flux will pass through the cube if the charge enclosed is the maximum (from Gauss' Law).
Thus, for enclosing maximum charge, the string should lie along the diagonal of length, $\sqrt{3}a$
Total charge, enclosed will $\sqrt{3}a\lambda$
So, the flux passing through the cube is,
$\varphi =\frac{\sqrt{3}\lambda a}{{ϵ}_0}$