Question

A cubical Gaussian surface encloses $30C$ per unit permittivity of charge. The electric flux through each face of the cube is:
A) $30C$
B) $15C$
C) $10C$
D) $5C$

Answer 1

In order to get the solution of the given question, we should be aware of Gaussian surface and its formula. The formula can be directly used to get the required solution. Since, in the question, it is given that the surface is a Gaussian surface, we need to find the flux for the entire cube and then find for each surface by dividing the total flux by six, as there are six surfaces in the cube. After that we will get the required solution to the given question.

Complete step by step solution:
It is given in the question that the total charge enclosed in the cube, $q = 30C$
Total flux on all the six faces, $\phi = \dfrac{{30}}{{{\varepsilon _0}}} = \dfrac{{{q_0}}}{{{\varepsilon _0}}}$
As we know that, from Gausses’ law, $\smallint E.dA = \dfrac{{{q_0}}}{{{\varepsilon _0}}}$
As in a cube, there are six surfaces,
Therefore, flux on each surface $= \dfrac{{30}}{{6{\varepsilon _0}}}$
$\Rightarrow \dfrac{{5C}}{{{\varepsilon _0}}}$

Hence, option (D), i.e. $5C$ is the correct solution.

Note: Electric flux is a property of an electric field that may be thought as the number of electric lines of force that intersect a given area. According to Gausses’ law, the distribution of electric charge to the resulting electric field is related. It is also known as gausses’ flux theorem. It also states that the total electric flux out of a closed surface is equal to the charge. Also, we know that electric flux is given by ${\phi _E} = E.S = ES\cos \theta$. Here $S$ is the surface area of the object. Electric flux is a way of describing the electric field strength at any distance from the charge that is causing the field.