Top PYQs of Electrostatic Potential and Capacitance for NEET

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Topic Question Set

Q 1 :
The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is [2018]

independent of the distance between the plates
linearly proportional to the distance between the plates
proportional to the square root of the distance between the plates
inversely proportional to the distance between the plates.

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(1)

Electrostatic force,

$F_{plate} = Q E = Q \times \frac{Q}{2 ε_{0} A} = \frac{Q^{2}}{2 A ε_{0}}$

$F$ is independent of the distance between plates.

Q 2 :
A parallel plate air capacitor has capacity $C$ , distance of separation between plates is $d$ , and potential difference $V$ is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is [2015]

$\frac{C V^{2}}{d}$
$\frac{C^{2} V^{2}}{2 d^{2}}$
$\frac{C^{2} V^{2}}{2 d}$
$\frac{C V^{2}}{2 d}$

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(4)

Force of attraction between the plates of the parallel plate air capacitor is $F = \frac{Q^{2}}{2 ε_{0} A}$

where $Q$ is the charge on the capacitor, $ε_{0}$ is the permittivity of free space, and $A$ is the area of each plate.

But $Q = C V$ and $C = \frac{ε_{0} A}{d}$ or $ε_{0} A = C d$

$∴$ $F = \frac{C^{2} V^{2}}{2 C d} = \frac{C V^{2}}{2 d}$

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