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 $\left(\frac{d}{2} \leq x \leq d\right)$
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 $\left(\frac{d}{2} \leq x \leq d\right)$
- [JEE MAIN 2021]
- A
$0$
- B
$\frac{{kA}}{2 \ln \left(\frac{2 \varepsilon_{0}+{kd}}{2 \varepsilon_{0}}\right)}$
- C
$\left(\varepsilon_{0}+\frac{{kd}}{2}\right)^{2 / / {kA}}$
- D
$\frac{{kA}}{2} \ln \left(\frac{2 \varepsilon_{0}}{2 \varepsilon_{0}-{kd}}\right)$
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