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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 the permittivity of dielectric varies as : ε(x) = ε₀ + kx, for (0 ≤ x ≤ d/2) ε(x) = ε₀ + k(d−x), for (d/2 ≤ x ≤ d)

1. (ε₀ + kd/2)^(2/kA)
2. kA / (2 ln((2ε₀ + kd)/(2ε₀)))
3. 0
4. (kA/2) ln((2ε₀)/(2ε₀ − kd))

Correct answer: 0

Solution

The capacity of the capacitor is determined by the effective permittivity of the dielectric material between the plates. In this case, the permittivity varies linearly and results in a configuration where the contributions from both halves of the dielectric cancel each other out, leading to a net capacitance of zero.

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