Question

A charge $Q$ is placed at the centre of a imaginary hemispherical surface. Using symmetry arguments and Gauss's law, find the flux of the electric field due to this charge through the curved surface of the hemisphere as shown in the figure.

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

Answer 1

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

Consider an imaginary upper hemisphere so that the charge $Q$ is now enclosed within a sphere.


Clearly, the charge $Q$ is symmetrically located with respect to both the hemispheres.

Thus, flux through upper hemisphere is equal to that through lower hemisphere because of symmetry.

By Gauss's Law,
Flux through the entire sphere$\varphi =\left(\frac{Q}{{\epsilon }_0}\right)$

$\therefore$ Flux through the lower hemisphere$=\frac{1}{2}\left(\frac{Q}{{\epsilon }_0}\right)$

Hence, option (b) is the correct answer.