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Home » A parallel plate air capacitor has capacity ‘ , distance of separation between plates is ‘d’ and potential difference ‘ is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is: (1) (2) (3) (4)
A parallel plate air capacitor has capacity ‘ C^{\prime}, distance of separation between plates is ‘d’ and potential difference ‘ V^{\prime} is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is: (1) \frac{c^{2} \mathrm{v}^{2}}{2 \mathrm{~d}^{2}} (2) \frac{c^{2} v^{2}}{2 d} (3) \frac{\mathrm{cV}^{2}}{2 \mathrm{~d}} (4) \frac{\mathrm{CV}^{2}}{\mathrm{~d}}
Physics | Physics
A parallel plate air capacitor has capacity ‘ C^{\prime}, distance of separation between plates is ‘d’ and potential difference ‘ V^{\prime} is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is: (1) \frac{c^{2} \mathrm{v}^{2}}{2 \mathrm{~d}^{2}} (2) \frac{c^{2} v^{2}}{2 d} (3) \frac{\mathrm{cV}^{2}}{2 \mathrm{~d}} (4) \frac{\mathrm{CV}^{2}}{\mathrm{~d}}

The Solution is  (3)
Attraction between the plates
\mathrm{F}=\frac{\mathrm{C}^{2} \mathrm{~V}^{2}}{2 \mathrm{Cd}}=\frac{\mathrm{CV}^{2}}{2 \mathrm{~d}}

Force of attraction between the plates is \mathrm{F}=\frac{\mathrm{Q}^{2}}{2 \mathrm{~A} \epsilon_{0}} or \mathrm{F}=\frac{\mathrm{C}^{2} \mathrm{~V}^{2}}{2 \mathrm{~A} \epsilon_{0}} \quad where \mathrm{Q}=\mathrm{CV}
also \mathrm{C}=\frac{\mathrm{A} \epsilon_{0}}{\mathrm{~d}} \Rightarrow \mathrm{A} \epsilon_{0}=\mathrm{Cd}
now, \mathrm{F}=\frac{\mathrm{C}^{2} \mathrm{~V}^{2}}{2 \mathrm{Cd}}=\frac{\mathrm{CV}^{2}}{2 \mathrm{~d}}

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