In figure shown, two parallel plate capacitors with fixed plates and connected to two batteries. The separation between the plates is same for the two capacitors. The plates are rectangular in shape with width b and length `l_(1)` and `l_(2)`, the separation between plates is d. The left half of the dielectric slab has a dielectric constant `K_(1)` and the right half `K_(2)(K_(2) gt K_(1))`. WMF of the right battery is greater then left battery. Neglecting any friction, find the extension in spring in equilibrium (spring is nonconducting) `(epsilon_(2) gt epsilon_(1))`

Answer

`(in_(0)b)/(2dK_(s))[(K_(2)-1)epsilon_(2)^(2)-(K_(1)-1)epsilon_(1)^(2)]`