A) \[\frac{1}{2}\left( \frac{q}{{{\varepsilon }_{0}}}-\phi \right)\]
B) \[\frac{q}{2\,{{\varepsilon }_{0}}}\]
C) \[\frac{\phi }{3}\]
D) \[\frac{q}{\,{{\varepsilon }_{0}}}-\phi \]
Correct Answer: A
Solution :
By Gauss?s Law \[{{\phi }_{total}}=\frac{q}{{{\varepsilon }_{0}}}\] Let flux corresponding to A B and C is \[{{\phi }_{A}},\,\,{{\phi }_{B}}\,\,and\,\,\phi C\] From symmetry of the figure \[{{\phi }_{C}}={{\phi }_{A}}\] \[\Rightarrow \] Now we can write \[{{\phi }_{total}}={{\phi }_{A}}+{{\phi }_{B}}+{{\phi }_{C}}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,2{{\phi }_{A}}+\phi =\frac{q}{{{\varepsilon }_{0}}}\,\,\,\,\Rightarrow \,\,\,{{\phi }_{A}}=\frac{1}{2}\,\left( \frac{q}{{{\varepsilon }_{0}}}-\phi \right)\]
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