A parallel plate capacitor with plate area ' A ' and distance of...

Taking an element of width dx at a distance $x$\left(x < d / 2\right)$from left plate </p><p>$dc = \dfrac{( {ε}_{0} + kx )A}{dx}$</p><p>Capacitance of half of the capacitor </p><p>$\dfrac{1}{C} = {∫}_{0}^{d / 2}\dfrac{1}{dc} = \dfrac{1}{A}{∫}_{0}^{d / 2}\dfrac{dx}{{ε}_{0} + kx}$</p><p>$\dfrac{1}{C} = \dfrac{1}{kA}\ln \left(\dfrac{{ε}_{0} + kd / 2}{{ε}_{0}}\right)$</p><p>Capacitance of second half will be same</p><p>${C}_{eq} = \dfrac{C}{2} = \dfrac{kA}{2\ln \left(\dfrac{2{ε}_{0} + kd}{2{ε}_{0}}\right)}