Flux through a cube of side a if a point charge of q is at one of its comer?

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1. Electric Charges and Fields

easy

What is the flux through a cube of side $a$ if a point charge of $q$ is at one of its comer?

A

$\frac{Q}{{6{\varepsilon _0}}}$

B

$\;\frac{Q}{{8{\varepsilon _0}}}$

C

$\;\frac{Q}{{3{\varepsilon _0}}}$

D

$\;\frac{Q}{{2{\varepsilon _0}}}$

(AIPMT-2012)

Solution

Eight identical cubes are required so that the given charge $q$ appears at the centre of the bigger cube.

Thus, the electric flux passing through the given cube is

$\phi = \frac{1}{8}\left( {\frac{q}{{{\varepsilon _0}}}} \right) = \frac{q}{{8{\varepsilon _0}}}$

Standard 12

Physics

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