Question

A point charge $Q$ is located just above the centre $\text{O}$ of the flat face of a hemisphere as shown in the figure. The electric flux through the flat face is

• A. $\frac{Q}{2{ϵ}_0}$
• B. $\frac{-Q}{2{ϵ}_0}$
• C. $\frac{Q}{{ϵ}_0}$
• D. $\frac{-Q}{{ϵ}_0}$

Answer 1

The correct option is B $\frac{-Q}{2{ϵ}_0}$

The enclose the charge $Q$, we can assume another hemisphere kept above the given hemisphere as shown in the figure.


Now, by Gauss's law, electric flux through the closed surface will be,

$\varphi =\frac{q_{\text{enclosed}}}{{ϵ}_o}=\frac{Q}{{ϵ}_0}$

Further through given flat face of hemisphere, electric flux will be,

$\varphi =\frac{-Q}{2{ϵ}_o}$ [By symmetry]

Here negative sign arises because the positive normal to the flat face is outwards (along $+y$ - axis) and electric field through $\text{O}$ is along $-y$ - axis.