A) \[\frac{q}{{{\varepsilon }_{0}}}\]
B) \[\frac{q}{3{{\varepsilon }_{0}}}\]
C) \[\frac{q}{6\,{{\varepsilon }_{0}}}\]
D) \[\frac{q}{8\,{{\varepsilon }_{0}}}\]
Correct Answer: D
Solution :
According to Gauss's law, the electric flux through a closed surface is equal to \[\frac{1}{{{\varepsilon }_{0}}}\]times the net charge enclosed by the surface. Since, q is the charge enclosed by the surface, then electric flux \[\phi =\frac{q}{{{\varepsilon }_{0}}}\] If charge q is placed at a corner of cube, it will be divided into 8 such cubes. Therefore, electric flux through the cube is \[\phi '=\frac{1}{8}\left( \frac{q}{{{\varepsilon }_{0}}} \right)\]
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