Question

An electric charge q is placed at the centre of the open end of a hollow cylindrical vessel of length $l$ and radius r. Then, the flux coming out of the surface of the cylinder is :

• A. $q/{\epsilon }_0$
• B. $\frac{q}{{\epsilon }_0}(\pi r^2+2\pi rl)$
• C. $q/2{\epsilon }_0$
• D. zero

Answer 1

The correct option is C $q/2{\epsilon }_0$

The charge enclosed by the cylinder is $Q_{en}=q/2$.
Using Gauss's law, the flux $\varphi =\frac{Q_{en}}{{ϵ}_0}=\frac{q}{2{ϵ}_0}$