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. $\frac{q}{\varepsilon_{0}}$
• B. $\frac{q}{6\varepsilon_{0}}$
• C. $\frac{q}{3\varepsilon_{0}}$
• 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
$\phi=\frac{1}{\varepsilon_{0}} q$
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
$\phi_{F}=\frac{1}{6} \phi=\frac{q}{6 \varepsilon_{0}}$