Question

A charge of $9\times {10}^{-8}\text{C}$ is distributed uniformly on the surface of a sphere of radius $1\text{cm}$. It is covered by a concentric, hollow conducting sphere of radius $5\text{cm}$. Find the electric flux through the hollow sphere.
(Take ${ϵ}_o=9\times {10}^{-12}{\text{C}}^2/{\text{N-m}}^2$)

• A. ${10}^2{\text{N-m}}^2/\text{C}$
• B. ${10}^3{\text{N-m}}^2/\text{C}$
• C. ${10}^4{\text{N-m}}^2/\text{C}$
• D. ${10}^5{\text{N-m}}^2/\text{C}$

Answer 1

The correct option is C ${10}^4{\text{N-m}}^2/\text{C}$

Given:
Charge, $q=9\times {10}^{-8}\text{C}$


Charge $q=9\times {10}^{-8}\text{C}$ is enclosed by a hollow sphere.

Thus, electric flux through a sphere can be calculated by Gauss's law

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

$\Rightarrow \varphi =\frac{9\times {10}^{-8}}{9\times {10}^{-12}}={10}^4{\text{N-m}}^2/\text{C}$

So, option $\left(c\right)$ is correct.