A) \[{{R}_{L}}\]
B) \[\phi \]
C) \[\frac{1}{2}\left( \frac{q}{{{\varepsilon }_{0}}}-\phi \right)\]
D) \[\frac{q}{2{{\varepsilon }_{0}}}\]
Correct Answer: A
Solution :
Key Idea Apply Gausss law to calculate the charge associated with plane surface A. Gausss law states that the net electric flux through any closed surface is equal to the net charge inside the surface divided by sq. ie. \[\sqrt{2}qa\] Let electric flux linked with surfaces A, B and C are \[qa\] and \[\sqrt{2}qa\]respectively. That is \[\frac{a}{2}\] Since, \[\frac{1}{4}\] \[\frac{1}{2}\] \[\sqrt{2}{{I}_{AC}}={{I}_{EF}}\] or \[{{I}_{AD}}=3{{I}_{EF}}\] But \[{{I}_{AC}}={{I}_{EF}}\] (given) Hence, \[{{I}_{AC}}=\sqrt{2}{{I}_{EF}}\]
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