#### Question - 6

Calculate the capacitance of a parallel plate condenser, with plate area A and distance between plates 4 when filled with a dielectric whose dielectric constant varies as:

\(( \epsilon(x)=\epsilon_{0}+\beta x, 0
\)

\((\epsilon(x)=\epsilon_{0}+\beta(d-x), \frac{d}{2}\)

For what value of would the capacity of the condenser twice that when it is without any dielectric?

- A \(\beta=\frac{4 \in_{0}}{d} \ln \left(\frac{\epsilon_{0}+\beta \frac{d}{2}}{\epsilon_{0}}\right)\)
- B \(\beta=\frac{\epsilon_{0}}{d} \ln \left(\frac{\epsilon_{0}+\beta \frac{d}{2}}{\epsilon_{0}}\right)\)
- C \(\beta=\frac{\epsilon_{0}}{2 d} \ln \left(\frac{\epsilon_{0}+2 \beta D}{\epsilon_{0}}\right)\)
- D \(\beta=\frac{\epsilon_{0}}{4 d} \ln \left(\frac{\epsilon_{0}+\beta D}{\epsilon_{0}}\right)\)