question_answer

A disk of radius \[a/4\] having a uniformly distributed charge 6 C is placed in the \[x-y\] plane with its centre at \[(-a/2,0,0)\]. A rod of length a carrying a uniformly distributed charge 8 C is placed on the x - axis from \[x=a/4\] to \[x=5a/4\]. Two point charges \[-7C\] and 3 C 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 :

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 \[\phi =\frac{{{q}_{in}}}{{{\varepsilon }_{0}}}=\frac{-2C}{{{\varepsilon }_{0}}}\,\,\,\,\,\,\,\,[{{q}_{in}}=-2C]\]