Question

There is a point charge q located at the centre of a cube. What is the electric flux of this point charge, through a face of the cube?

• A. $\frac{q}{{\epsilon }_0}$
• B. $\frac{q}{6{\epsilon }_0}$
• C. $\frac{q}{3{\epsilon }_0}$
• D. It will depend upon the size of the cube

Answer 1

Answer: (B)

According to Gauss’s law
Electric flux linked with a cube enclosing a charge q is
$\varphi =\frac{1}{{\epsilon }_0}q$
As cube is a symmetrical body with 6-faces and the point charge is at its centre, so electric flux linked with each face is
${\varphi }_F=\frac{1}{6}\varphi =\frac{q}{6{\epsilon }_0}$