Question

A charge $Q$ is placed at the outer side of a cube at on corner. Find the flux passing through a face adjoining the charge :

• A. $\frac{Q}{6{\epsilon }_0}$
• B. $\frac{Q}{8{\epsilon }_0}$
• C. $\frac{Q}{24{\epsilon }_0}$
• D. $\frac{Q}{32{\epsilon }_0}$

Answer 1

Answer: (C)

$\frac{Q}{24{\epsilon }_0}$

The charge will be completely covered by 8 cubes

$\therefore \oint E.ds=\frac{Q_{enclosed}}{{\epsilon }_0}$ or

$E\left(8a^2\right)=\frac{Q}{{\epsilon }_0}$ or $E{a}^2=\frac{Q}{8{\epsilon }_0}$

3 faces of each cube will share the flux. Hence 24 faces in all will share the flux

$3E_0\left(a^2\right)=\frac{Q}{{\epsilon }_0}$ or $E_0{a}^2=\frac{Q}{24{\epsilon }_0}$