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 : \(\varepsilon(x)=\varepsilon_{0}+k x, \text { for }\left(0\,<\,x \leq \frac{d}{2}\right)\) \(\varepsilon(x)=\varepsilon_{0}+k(d-x)\), for \(\left(\frac{d}{2} \leq x \leq d\right)\)

1. A \(0\)
2. B \(\frac{{kA}}{2 \ln \left(\frac{2 \varepsilon_{0}+{kd}}{2 \varepsilon_{0}}\right)}\)
3. C \(\left(\varepsilon_{0}+\frac{{kd}}{2}\right)^{2 / / {kA}}\)
4. D \(\frac{{kA}}{2} \ln \left(\frac{2 \varepsilon_{0}}{2 \varepsilon_{0}-{kd}}\right)\)