A) \[\frac{q}{2{{\varepsilon }_{0}}}\]
B) \[\frac{\phi }{3}\]
C) \[\frac{q}{{{\varepsilon }_{0}}}-\phi \]
D) \[\frac{1}{2}\left( \frac{q}{{{\varepsilon }_{0}}}-\phi \right)\]
Correct Answer: D
Solution :
[d] Since \[{{\phi }_{total}}={{\phi }_{A}}+{{\phi }_{B}}+{{\phi }_{C}}=\frac{q}{{{\varepsilon }_{0}}},\] where \[q\] is the total charge. As shown in the figure, flux associated with the curved surface B is \[\phi ={{\phi }_{B}}\] Let us assume flux linked with the plane surfaces A and C be \[{{\phi }_{A}}={{\phi }_{C}}=\phi '\] Therefore, \[\frac{q}{{{\varepsilon }_{0}}}=2\phi '+{{\phi }_{B}}=2\phi '+\phi \]\[\Rightarrow \]\[\phi '=\frac{1}{2}\left( \frac{q}{{{\varepsilon }_{0}}}-\phi \right)\]
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