A) \[\frac{{{C}^{2}}{{V}^{2}}}{2d}\]
B) \[\frac{C{{V}^{2}}}{2d}\]
C) \[\frac{C{{V}^{2}}}{d}\]
D) \[\frac{{{C}^{2}}{{V}^{2}}}{2{{d}^{2}}}\]
Correct Answer: A
Solution :
Force between plates of parallel capacitor, \[F=qE=q\left[ \frac{\sigma }{2{{\varepsilon }_{0}}} \right]\] \[\because \] Surface charge density \[\sigma =\frac{\sigma }{A}\] \[\therefore \,\,\,\,\,\,\,F=q\left[ \frac{q}{2A{{\varepsilon }_{0}}} \right]\Rightarrow F=\frac{{{q}^{2}}}{2A{{\varepsilon }_{0}}}\] So, net charge across a capacitor, \[q=CV\] \[F=\frac{{{C}^{2}}{{V}^{2}}}{2A{{\varepsilon }_{0}}}\] \[\left[ C=\frac{A{{\varepsilon }_{0}}}{d} \right]\] \[F=\frac{\left( \frac{A{{\varepsilon }_{0}}}{d} \right)\times C{{V}^{2}}}{2A{{\varepsilon }_{0}}}=\frac{C{{V}^{2}}}{2d}\]
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