# What is the flux through a cube of side 'a' if a point charge of 'q' is at one of its corner? Option 1) $\frac{2q}{\varepsilon _0}$ Option 2) $\frac{q}{8\varepsilon _0}$ Option 3) $\frac{q}{\varepsilon _0}$ Option 4) $\frac{q}{2\varepsilon _0}$

D Divya Saini

As we learnt in

Gauss's Law -

Total flux linked with a closed surface called Gaussian surface.

Formula:

$\dpi{100} \phi = \oint \vec{E}\cdot d\vec{s}=\frac{Q_{enc}}{\epsilon _{0}}$

- wherein

No need to be a real physical surface.

Qenc - charge enclosed by closed surface.

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

$\therefore \phi = \frac{1}{8}\left \lfloor \frac{q}{\varepsilon _{0}} \right \rfloor =\frac{q}{8\varepsilon _{0}}$

Option 1)

$\frac{2q}{\varepsilon _0}$

Incorrect

Option 2)

$\frac{q}{8\varepsilon _0}$

Correct

Option 3)

$\frac{q}{\varepsilon _0}$

Incorrect

Option 4)

$\frac{q}{2\varepsilon _0}$

Incorrect

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