A) \[8{{\varepsilon }_{0}}\]
B) \[2{{\varepsilon }_{0}}\]
C) \[3{{\varepsilon }_{0}}\]
D) \[5{{\varepsilon }_{0}}\]
Correct Answer: A
Solution :
From Gauss's law, "the net electric flux through any closed surface is equal to the net charge inside the surface divided by \[{{\varepsilon }_{0}}\].? Then \[\mathop{\int\mkern-20.8mu \circlearrowleft} \overrightarrow{E} .\overrightarrow{dS}=\frac{{{q}_{in}}}{{{\varepsilon }_{0}}}\] \[\therefore \]\[100\times {{(0.2)}^{2}}-(100){{(0.2)}^{2}}+0+0=\frac{{{q}_{in}}}{{{\varepsilon }_{0}}}\] \[\Rightarrow \] \[4-(-4)=\frac{{{q}_{in}}}{{{\varepsilon }_{0}}}\] \[\therefore \] \[{{q}_{in}}=8\,{{\varepsilon }_{0}}\]
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