First slide

Capacitance

Question

One plate of a capacitor is fixed, and the other is connected to a spring as shown in Fig. Area of both the plates is A. In steady state (equilibrium), separation between the plates is 0.8d (spring was unstretched, and the distance between the plates was d when the capacitor was uncharged). The force constant of the spring is approximately

Moderate

A

$\frac{125}{32} \frac{ε_{0} A E^{2}}{d^{3}}$
B

$\frac{2 ε_{0} A E^{2}}{d^{3}}$
C

$\frac{6 ε_{0} E^{2}}{A d^{2}}$
D

$\frac{ε_{0} A E^{3}}{2 d^{3}}$

Solution

F = Kx $\Rightarrow$ $\frac{Q^{2}}{2 A ε_{0}} = K (0.2 d)$ $\Rightarrow$ $\frac{{(\frac{ε_{0} A}{0.8 d} E)}^{2}}{2 Α ε_{0}} = 0.2 K d$ $\Rightarrow$ $K = 4 ε_{0} A E^{2} / d^{3}$

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