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What is the flux through a cube of side 'a' if a point charge of q is at one of its corner?
A
$\frac{q}{2\varepsilon_0}6a^2$
B
$\frac{2q}{\varepsilon_0}$
C
$\frac{q}{8\varepsilon_0}$
D
$\frac{q}{\varepsilon_0}$
Detailed Solution
A charge at a corner is shared equally by 8 cubes that meet at that corner.
By Gauss's theorem the total flux from the charge is $\frac{q}{\varepsilon_0}$.
Flux through one cube $= \frac{1}{8}\times\frac{q}{\varepsilon_0} = \frac{q}{8\varepsilon_0}$
By Gauss's theorem the total flux from the charge is $\frac{q}{\varepsilon_0}$.
Flux through one cube $= \frac{1}{8}\times\frac{q}{\varepsilon_0} = \frac{q}{8\varepsilon_0}$