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

Options

A. `(125)/(32) (epsilon_(0)AE^(2))/d^(3)`
B. `(2epsilon_(0)AE^(2))/d^(3)`
C. `(6epsilon_(0)E^(2))/(Ad^(2))`
D. `(epsilon_(0)AE^(3))/(2d^(3))`

Answer

A

Explanation

`F=Kx`
`Q^(2)/(2Aepsilon_(0))=K(0.2d)`
or
or `((epsilon_(0)A)/(0.8d)E)^(3)/(2Aepsi_(0))=0.2 Kd`
or `K=3.9 epsilon_(0)AE^(2)//d^(3)`
`K=4epsilon_(0)AE ^(2)//d^(3)`.