Question

A charge q is placed at the centre of a cubical box of side a with top open. The flux of electric field through the surface of the cubical box is:

• A. zero
• B. $q/{\epsilon }_0$
• C. $q/6{\epsilon }_0$
• D. $5q/6{\epsilon }_0$

Answer 1

The correct option is D $5q/6{\epsilon }_0$

because charge is placed at the centre of the box, by symmetry we can say that,
${\varphi }_{eachface}=\frac{1}{6}{\varphi }_{total}$
now, if the box were complete
total flux passing through it would be
$=\frac{q}{{ϵ}_0}$
but since it has one face missing,
$flux=5\times \frac{1}{6}\frac{q}{{ϵ}_0}$
$=\frac{5q}{6{ϵ}_0}$