Question

Find the flux of the electric field through a spherical surface of radius $R$ due to a charge of ${10}^{-7}\text{C}$ at the centre and another equal charge at a point $2R$ away from the centre.
(Take ${ϵ}_o=9\times {10}^{-12}{\text{C}}^2/{\text{N-m}}^2$ )

• A. $3.1\times {10}^4{\text{N-m}}^2/\text{C}$
• B. $2.1\times {10}^4{\text{N-m}}^2/\text{C}$
• C. $1.1\times {10}^4{\text{N-m}}^2/\text{C}$
• D. $4.1\times {10}^4{\text{N-m}}^2/\text{C}$

Answer 1

The correct option is C $1.1\times {10}^4{\text{N-m}}^2/\text{C}$

We know that from Gauss's law, electric flux through a closed surface is,

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

Here, only one charge is enclosed by the spherical surface.

So, $q_{\text{enclosed}}={10}^{-7}\text{C}$

$\Rightarrow \varphi =\frac{{10}^{-7}}{9\times {10}^{-12}}$

$\Rightarrow \varphi =1.1\times {10}^4{\text{N-m}}^2/\text{C}$