Question
What is the flux through a cube of side $$a$$ if a point charge of $$q$$ is at one of its corner?
A.
$$\frac{{2q}}{{{\varepsilon _0}}}$$
B.
$$\frac{q}{{8{\varepsilon _0}}}$$
C.
$$\frac{q}{{{\varepsilon _0}}}$$
D.
$$\frac{q}{{2{\varepsilon _0}}}6{a^2}$$
Answer :
$$\frac{q}{{8{\varepsilon _0}}}$$
Solution :
According to Gauss's law, the electric flux through a closed surface is equal to $$\frac{1}{{{\varepsilon _0}}}$$ times the net charge enclosed by the surface.
As the charge enclosed $$ = \frac{q}{8}$$
So, electric flux $$ = \frac{{{q_{{\text{enclosed}}}}}}{{{\varepsilon _0}}} \Rightarrow \phi = \frac{q}{{8{\varepsilon _0}}}$$