A) \[\frac{q}{{{\varepsilon }_{0}}}\]
B) \[\frac{q}{\pi {{\varepsilon }_{0}}}\]
C) \[\frac{q}{4{{\varepsilon }_{0}}}\]
D) \[\frac{q}{6{{\varepsilon }_{0}}}\]
Correct Answer: D
Solution :
(d) \[\frac{q}{6{{\varepsilon }_{0}}}\] An imaginary cube can be made by considering charge 'q' at the centre and given square is one of its face. From Gauss Law, \[\phi =\frac{{{Q}_{in}}}{{{\varepsilon }_{0}}}\] This is the flux passing through all the six surfaces. \[\therefore \,\,\,\frac{1}{6}\]th of this flux would pass through one surface.
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