Question
A charge $$q$$ is placed at the corner of a cube of side $$a.$$ The electric flux through the cube is
A.
$$\frac{q}{{{\varepsilon _0}}}$$
B.
$$\frac{q}{{3{\varepsilon _0}}}$$
C.
$$\frac{q}{{6{\varepsilon _0}}}$$
D.
$$\frac{q}{{8{\varepsilon _0}}}$$
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.
Since, $$q$$ is the charge enclosed by the surface, then electric flux, $$\phi = \frac{q}{{{\varepsilon _0}}}$$
If charge $$q$$ is placed at a corner of cube, it will be divided into 8 such cubes. Therefore, electric flux through the cube is $$\phi ' = \frac{1}{8}\left( {\frac{q}{{{\varepsilon _0}}}} \right)$$