A) \[{{\in }_{0}}{{E}^{2}}Ad\]
B) \[\frac{1}{2}{{\in }_{0}}{{E}^{2}}Ad\]
C) \[\frac{1}{2}{{\in }_{0}}{{E}^{2}}/Ad\]
D) \[{{\varepsilon }_{0}}{{E}^{2}}/Ad\]
Correct Answer: A
Solution :
[a] Energy required to charge the capacitor is \[W=U=QV\] \[\Rightarrow U=C{{V}^{2}}=\frac{{{\varepsilon }_{0}}A}{d}{{y}^{2}}=\frac{{{\varepsilon }_{0}}Ad}{{{d}^{2}}}\] \[{{V}^{2}}={{\varepsilon }_{0}}{{E}^{2}}Ad\text{ }\left[ \because E=\frac{V}{d} \right]\]
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