Question

A charge $Q$ is uniformly distributed over a rod of length $L$. Consider a hypothetical sphere of radius $\frac{L}{2}$ with the centre of the sphere at one end of the rod. Find the value of flux passing through the entire surface of the sphere.

• A. $\frac{Q}{2{\epsilon }_0}$
• B. $\frac{Q}{{\epsilon }_0}$
• C. $\frac{Q}{3{\epsilon }_0}$
• D. $\frac{2Q}{{\epsilon }_0}$

Answer 1

The correct option is A $\frac{Q}{2{\epsilon }_0}$

As charges $Q$ is uniformly distributed over the length of the rod, hence net charge enclosed by the spherical shell $Q_{in}=\frac{Q}{2}$


By Gauss's Law, the flux through the spherical shell,

$\varphi =\frac{Q_{in}}{{\epsilon }_0}=\frac{Q}{2{\epsilon }_0}$

Hence, option (c) is the correct answer.