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A charge Q $\mu C$ is placed at the centre of a cube, the flux coming out from any surface will be : -
A
$\dfrac{Q}{6\varepsilon_0} \times 10^{-6}$
B
$\dfrac{Q}{6\varepsilon_0} \times 10^{-3}$
C
$\dfrac{Q}{2\varepsilon_0}$
D
$\dfrac{Q}{8\varepsilon_0}$
Detailed Solution
By Gauss's law, the total flux through the cube $= \dfrac{q}{\varepsilon_0}$.
The charge is at the centre, so by symmetry each of the 6 faces gets an equal share: flux through one face $= \dfrac{q}{6\varepsilon_0}$.
The charge is Q $\mu C$ $= Q \times 10^{-6}$ C.
Flux through any face $= \dfrac{Q}{6\varepsilon_0} \times 10^{-6}$
The charge is at the centre, so by symmetry each of the 6 faces gets an equal share: flux through one face $= \dfrac{q}{6\varepsilon_0}$.
The charge is Q $\mu C$ $= Q \times 10^{-6}$ C.
Flux through any face $= \dfrac{Q}{6\varepsilon_0} \times 10^{-6}$