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  4. A point charge + q is placed at the mid point of a cube of side L . The electric flux emerging from the cube is :

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Q. A point charge $ + q $ is placed at the mid point of a cube of side $ L $ . The electric flux emerging from the cube is :

UPSEEUPSEE 2005

Solution:

From Gauss theorem, the electric flux $(\phi)$ through any closed surface is equal to $\frac{1}{\varepsilon_{0}}$ times the net charge $q$ enclosed by the surface. Thus,
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$\phi=\int \vec{ E } \cdot d \vec{ A }=\frac{q}{\varepsilon_{0}}$