A) \[\frac{4\pi q}{6(4\pi {{\varepsilon }_{0}})}\]
B) \[\frac{\pi q}{6(4\pi {{\varepsilon }_{0}})}\]
C) \[\frac{q}{6(4\pi {{\varepsilon }_{0}})}\]
D) \[\frac{2\pi q}{6(4\pi {{\varepsilon }_{0}})}\]
Correct Answer: A
Solution :
According to Gausss theorem, electric flux through the cube (closed surface), \[\text{o }\!\!|\!\!\text{ =}\frac{q}{{{\varepsilon }_{0}}}\] Since, cube has six surfaces and all the faces are symmetrical, therefore electric flux through any face \[\text{o }\!\!|\!\!\text{ }\!\!\!\!\text{ }\,\text{=}\frac{q}{6{{\varepsilon }_{0}}}=\frac{4\pi q}{6(4\pi {{\varepsilon }_{0}})}\]
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