Question

A charge $q$ is placed at the corner of a cube of side $a$ . The electric flux through the cube is

• A. $\frac{q}{{\epsilon }_0}$
• B. $\frac{q}{3{\epsilon }_0}$
• C. $\frac{q}{6{\epsilon }_0}$
• D. $\frac{q}{8{\epsilon }_0}$

Answer 1

Answer: (D)

According to Gauss's law, the electric flux through a closed surface is equal to $\frac{1}{{\epsilon }_0}$ times the net charge enclosed by the surface. Since, q is the charge enclosed by the surface, then the electric flux $\varphi =\frac{q}{{\epsilon }_0}$
If charge q is placed at a comer of cube, it will be divided into 8 such cubes. Therefore, electric flux through the cube is
${\varphi }^{\prime }=\frac{1}{8}\left(\frac{q}{{\epsilon }_0}\right)$