A parallel plate capacitor is made of two square plates of side a , separated by a distance d d ≪ a . The lower triangular portion filled with a dielectric of dielectric constant K , as shown in the figure. Capacitance of this capacitor is:

Question

A parallel plate capacitor is made of two square plates of side a , separated by a distance d d ≪ a . The lower triangular portion filled with a dielectric of dielectric constant K , as shown in the figure. Capacitance of this capacitor is:, K ε 0 a 2 2 d K + 1, K ε 0 a 2 d K - 1 ln ⁡ K, K ε 0 a 2 d ln ⁡ K, 1 2 K ε 0 a 2 d

MARKS App · Accepted Answer

Consider a small element at a distance x. It is a two capacitors in series. d c = d c 1 × d c 2 d c 1 + d c 2 d c = ε 0 . a d x x t a n θ k + d - x t a n θ 1 ∴ d c = ε 0 K . a d x - x tan ⁡ θ K - 1 + d . k ∴ C = ∫ 0 a ε 0 K . a d x - x tan ⁡ θ K - 1 + d . k = ε 0 k . a tan ⁡ θ ( K - 1 ) l n - a tan ⁡ θ K - 1 + d . k d . K = ε 0 K a 2 d K - 1 l n K

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