A) \[\frac{\pi q}{6(4\pi {{\varepsilon }_{0}})}\]
B) \[\frac{q}{6(4\pi {{\varepsilon }_{0}})}\]
C) \[\frac{2\pi q}{6(4\pi {{\varepsilon }_{0}})}\]
D) \[\frac{4\pi q}{\frac{1}{6}(4\pi {{\varepsilon }_{0}})}\]
Correct Answer: D
Solution :
By Gauss law in electrostatics, electric flux through any closed surface is \[\frac{q}{{{\varepsilon }_{0}}}\]. If the charge is located at the centre of the cube it is placed symmetrically with respect to each other. \[\therefore \] Electric flux through each face is\[\frac{1}{6}\frac{q}{{{\varepsilon }_{0}}}=\frac{1}{6}\frac{4\pi q}{(4\pi {{\varepsilon }_{0}})}\]
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