Question

Consider two concentric spherical surfaces ${\text{S}}_1$ with radius $a$ and ${\text{S}}_2$ with radius $2a$, both centred on the origin. There is a charge $+q$ at the origin, and no other charges. Compare the flux ${\varphi }_1$ through ${\text{S}}_1$ with flux ${\varphi }_2$ through ${\text{S}}_2$

• A. ${\varphi }_1=2{\varphi }_2$
• B. ${\varphi }_1=4{\varphi }_2$
• C. ${\varphi }_1=\frac{{\varphi }_2}{2}$
• D. ${\varphi }_1={\varphi }_2$

Answer 1

The correct option is D ${\varphi }_1={\varphi }_2$

Flux through Gaussian surface
$\varphi =\frac{q_{\text{enc}}}{{\epsilon }_0}$

Therefore flux through any surface depends only on total charge inside the surface.

Although the two sphere have different dimensions, the charge enclosed by the spheres are same.
So, ${\varphi }_1={\varphi }_2=\frac{q_{\text{enc}}}{{\epsilon }_0}$

Hence, option (c) is correct answer.