Question

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

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

Answer 1

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

$\varphi =\frac{q}{{ϵ}_o}$

Now, for maximum flux, the length of string inside the flux should be maximum.

Hence,the string should be along the diagonal of the cube.

Length of string$=AB=\sqrt{3}l$

Hence,maximum flux$={\varphi }_{max}=\frac{q}{{ϵ}_o}$

And, charge=$q=\lambda \times AB$

Hence, ${\varphi }_{max}=\frac{\sqrt{3}\lambda l}{{ϵ}_o}$

Answer-(A)