The gap between the plates of a parallel plate capacitor of area A… | JEE Main 2014 (19 Apr, Shift 1)

Q106JEE Main 2014 · 19 APR · SHIFT 1Difficult

Dielectrics

The gap between the plates of a parallel plate capacitor of area A and distance between plates d, is filled with a dielectric whose permittivity varies linearly from $\epsilon$ 1 at one plate to $\epsilon$ 2 at the other. The capacitance of capacitor is:

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Answer: (d)

$\epsilon(x) = \epsilon_1 + \frac{(\epsilon_2 - \epsilon_1)x}{d}$ ; layers in series: $\frac{1}{C} = \int_0^d \frac{dx}{\epsilon_0 \epsilon(x) A}$ .
$\frac{1}{C} = \frac{d}{\epsilon_0 A(\epsilon_2 - \epsilon_1)}\ln\frac{\epsilon_2}{\epsilon_1}$
$C = \frac{\epsilon_0(\epsilon_2 - \epsilon_1)A}{d\ln(\epsilon_2/\epsilon_1)}$ , so the answer is (d).

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Dielectrics question from JEE Main 2014 (19 Apr, Shift 1)

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