A) \[\frac{q\times {{10}^{-6}}}{24{{\varepsilon }_{0}}}\]
B) \[\frac{q\times {{10}^{-4}}}{{{\varepsilon }_{0}}}\]
C) \[\frac{q\times {{10}^{-6}}}{6{{\varepsilon }_{0}}}\]
D) \[\frac{q\times {{10}^{-4}}}{12{{\varepsilon }_{0}}}\]
Correct Answer: C
Solution :
Key Idea: According to Gauss' law, total electric flux through a closed surface is equal to \[\frac{1}{{{\varepsilon }_{0}}}\] rimes the total charge enclosed by the surface. From key idea, the electric flux emerging from the cube is \[\phi =\frac{1}{{{\varepsilon }_{0}}}\times \text{charge}\,\,\text{enclosed}\] \[=\frac{1}{{{\varepsilon }_{0}}}\times q\times {{10}^{-6}}\] Since, a cube has six faces, so electric flux through each face is, \[\phi '=\frac{\phi }{6}=\frac{1}{6{{\varepsilon }_{0}}}\times q\times {{10}^{-6}}=\frac{q\times {{10}^{-6}}}{6{{\varepsilon }_{0}}}\]
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