question_answer

A disc of radius a/4 having a uniformly distributed charge 6C is placed in the x-y plane with its center at (-a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from \[x=a/4\] to \[x=5a/4\]. Two point charges -7C and 3C are placed at (a/4, -a/4, 0) and (-3a/4, 3a/4, 0), respectively. Consider a cubical surface formed by six surfaces \[x=\pm a/2,y=\pm a/2,z=\pm a/2.\] The electric flux through this cubical surface is

A) \[\frac{-2C}{{{\varepsilon }_{0}}}\]

B) \[\frac{2C}{{{\varepsilon }_{0}}}\]

C) \[\frac{10C}{{{\varepsilon }_{0}}}\]

D) \[\frac{12C}{{{\varepsilon }_{0}}}\]

Correct Answer: A

Solution :

[a] From the figure it is clear that the charge enclosed in the cubical surface is \[3C+2C-7C=-2C.\] Therefore the electric flux through the cube is      \[\phi =\frac{{{q}_{in}}}{{{\varepsilon }_{0}}}=\frac{-2C}{{{\varepsilon }_{0}}}\]