Question

A charge $Q\mu$ C is placed at the centre of cube, the flux coming out from any surface will be :

• A. $\frac{Q}{24{\epsilon }_0}$
• B. $\frac{Q}{8{\epsilon }_0}$
• C. $\frac{Q}{6{\epsilon }_0}\times 10^{-6}$
• D. $\frac{Q}{6{\epsilon }_0}\times 10^{-3}$

Answer 1

Answer: (C)

From Gauss theorem, the electric flux through any closed surface is equal to $\frac{1}{{\epsilon }_0}$ times the net charge $Q$ enclosed by the surface, that is,
${\varphi }_E=\int E\cdot dA=\frac{q}{{\epsilon }_0}$
Total flux through six faces of the cube is

$\varphi =\frac{Q\times 10^{-6}}{{\epsilon }_0}$
Since, cube has six faces, therefore flux through one face is
${\varphi }_s=\frac{1\times Q\times 10^{-6}}{6{\epsilon }_0}$
${\varphi }_s=\frac{Q\times 10^{-6}}{6{\epsilon }_0}\frac{N{m}^2}{C}$