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Question

One plate of a capacitor is connected to a spring as shown in figure. Area of both the plates is A. In steady state separation between the plates is 0.6 d (spring was to un stretched and the distance between the plates was d when the capacitor was uncharged. The force constant of the spring is

A
3.5ϵ0AE2d3
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B
2ϵ0AEd2
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C
6ϵ0E2A d3
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D
ϵ0AE22d3
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Solution

The correct option is A 3.5ϵ0AE2d3
In equilibrium electro static attraction between the plates = spring force
q22ϵ0A=kx
(CE)22ϵ0A=k(d0.6d)
(ϵ0A0.6d)2E22ϵ0A=0.4dk
k=ϵ0AE20.256d33.5ϵ0AE2d3

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