Question

A charge $Q$ is uniformly distributed over a rod of length $l$. Consider a hypothetical cube of edge $l$ with the centre of the cube at one end of the rod. Find the minimum possible flux of the electric field through the entire surface of the cube.

• A. $\frac{Q}{4{\epsilon }_0}$
• B. $\frac{2Q}{{\epsilon }_0}$
• C. $\frac{Q}{{\epsilon }_0}$
• D. $\frac{Q}{2{\epsilon }_0}$

Answer 1

Answer: (D)

$\frac{Q}{2{\epsilon }_0}$

Here, half of the length of the rod outside the cube. From Gauss's law, flux,$\varphi =\frac{Q_{en}}{{ϵ}_0}$
where $Q_{en}=$charge inside the cube$=\frac{Q}{2}$
thus, flux$\left(\varphi \right)=\frac{Q}{2{ϵ}_0}$