| ASSERTION: The force between the plates of parallel plate capacitor is proportional to charge on it. |
| REASON: Force is equal to charge per unit area per \[{{\in }_{0}}\]. |
A) If both assertion and reason are true and reason is the correct explanation of assertion.
B) If both assertion and reason are true and reason is not the correct explanation of assertion.
C) If assertion is true but reason is false.
D) If both assertion and reason are false.
E) If assertion is false but reason is true.
Correct Answer: D
Solution :
The potential energy stored between the plates of capacitor. \[U=\frac{1}{2}\frac{{{Q}^{2}}}{C}=\frac{1}{2}\frac{{{Q}^{2}}}{{{\varepsilon }_{0}}A}x\] \[\left( \because \,\,C=\frac{{{\varepsilon }_{0}}A}{x} \right)\] Force \[F=-\frac{\partial U}{\partial x}=-\frac{\partial }{\partial x}\left( \frac{1}{2}\frac{{{Q}^{2}}x}{{{\varepsilon }_{0}}A} \right)\] \[=-\frac{1}{2}\frac{{{Q}^{2}}}{{{\varepsilon }_{0}}A}=\frac{1}{2}\frac{{{\sigma }^{2}}}{{{\varepsilon }_{0}}}A\] Negative sign shows force is attractive.
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