An ideal gas is enclosed in a cylinder fitted with a frictionless piston. The piston is connected with a light rod to one plate of capacitor whose other plate is fixed as shown. Initially volume of the gas inside the cylinder is V₀. Atmospheric pressure is P₀, separation between the plates is L, area of the piston as well as of the capacitor plates is A and emf of battery is $\mathrm{\epsilon }$. A heater supplies heat to the gas so that pressure of the gas is given as $\mathrm{P}={\mathrm{P}}_0-\frac{{\mathrm{n\epsilon }}_0{\mathrm{\epsilon }}^2}{{\mathrm{L}}^2}$, when piston is displaced by a distance $\frac{\mathrm{L}}{2}$. Find value of n.