A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as :

ε(x)=ε0+kx, for (0ε(x)=e0+k(d−x), for (d/2≤x≤d)

A. (ε0+kd/2)²/ᵏᴬ
B. kA/2 ln(2ε0+kd/2ε₀)
C. 0
D. kA/2ln(2ε₀ / 2ε₀−kd)