Two charged capacitors have their outer plates fixed and inner plates connected . . .

Question : Two charged capacitors have their outer plates fixed and inner plates connected by a spring of force constant 'k'. The charge on each capacitor is q. Find the extension in the spring at equilibrium 

(1) q²/2Aε₀k
(2) q²/4Aε₀k
(3) q²/Aε₀k

(4) Zero 

Doubt by Saatvik

Solution : 

We know the forcce between the two plates of parallel plat capacitor is given by 
F=qE

F=q[σ/2ε₀]
F=q[(q/A)/2ε₀]
F=q²/[2Aε₀] — (1) 

Also 
Spring Force is given by 
|F|=kx — (2)

From equation (1) and (2) 
q²/[2Aε₀]=kx
q²/2Aε₀=kx
q²/2Aε₀k=x

x=q²/2Aε₀k

Hence, (1) q²/2Aε₀k, would be the correct option.