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A charge Q is situated at the corner of a cube, the electric flux passed through all the six faces of the cube is :
A
$\dfrac{Q}{6\varepsilon_0}$
B
$\dfrac{Q}{8\varepsilon_0}$
C
$\dfrac{Q}{\varepsilon_0}$
D
$\dfrac{Q}{2\varepsilon_0}$
Detailed Solution
Imagine 8 identical cubes placed around the corner, so that the charge is at the centre of a large cube made of 8 small cubes.
The total flux through the large closed surface is $\dfrac{Q}{\varepsilon_0}$, shared equally by the 8 small cubes.
So the flux through the given cube is $\dfrac{Q}{8\varepsilon_0}$.
(Three faces of the cube meet at the corner and have zero flux, since the field lines are parallel to them; all the flux passes through the other three faces.)
So the flux through all six faces is $\dfrac{Q}{8\varepsilon_0}$.
The total flux through the large closed surface is $\dfrac{Q}{\varepsilon_0}$, shared equally by the 8 small cubes.
So the flux through the given cube is $\dfrac{Q}{8\varepsilon_0}$.
(Three faces of the cube meet at the corner and have zero flux, since the field lines are parallel to them; all the flux passes through the other three faces.)
So the flux through all six faces is $\dfrac{Q}{8\varepsilon_0}$.