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) \[\frac{4\pi q}{6(4\pi {{\varepsilon }_{0}})}\]
Correct Answer: D
Solution :
Key Idea: Gauss's law states that, "the net electric flux through any closed surface is equal to the net charge inside the closed surface divided by\[{{\varepsilon }_{0}}''.\] From Gauss's law \[\phi =\frac{q}{{{\varepsilon }_{0}}}\] This is the net flux coming out of the cube. Since, a cube has 6 sides so electric flux through any face is \[\phi '=\frac{\phi }{6}=\frac{q}{6{{\varepsilon }_{0}}}=\frac{4\pi q}{6(4\pi {{\varepsilon }_{0}})}\]
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