Question

The inward and outward electric flux for a closed surface is $N{m}^2/C$are respectively $8\times {10}^3$and $4\times {10}^3$. Then the total charge inside the surface is ________ C.
(A) ${\displaystyle \frac{-4\times {10}^3}{{\epsilon }_0}}$
(B) $-4\times {10}^3$
(C) $4\times {10}^3$
(D) $4\times {10}^3{\epsilon }_0$

Answer 1

Hint We should know the amount of something, which can be electric field or any other physical quantity, that passes through the surface. The total amount of flux is dependent on the strength of the field, the size of the surface through which the flux is passing through and also the orientation.

Complete step by step answer
We know that according to the convention, the inward flux is always taken as negative and the outward flux is always taken as positive.
Hence we can say that the flux, which is denoted by $\varphi$is given as : $-8\times {10}^3+4\times {10}^3=-4\times {10}^{3}N{m}^2/C$
Now we know that, $\varphi$or the flux is denoted as ${\displaystyle \frac{q}{{\epsilon }_0}}$
So, we can evaluate to find that:
$\Rightarrow q=\varphi {\epsilon }_0$
$\Rightarrow q=-4\times {10}^3{\epsilon }_0$
Hence, we can say that the total charge inside the surface is $4\times {10}^3{\epsilon }_0$.

Hence the correct answer is option D.

$\Rightarrow q=\varphi {\epsilon }_0$
$\Rightarrow q=-4\times {10}^3{\epsilon }_0$

Note We should know that if we consider a closed surface then the orientation of the surface is usually defined as the flux which is flowing from the inside to the outside as positive in nature. This is also known as the inward flux. And the flux which is flowing from the outside to the inside, is considered as negative and is termed as the outward flux.