JEE Advanced2019PhysicsCapacitanceActual
A parallel plate capacitor of capacitance C has spacing d between two plates having area A . The region between the plates is filled with N dielectric layers, parallel to its plates, each with thickness δ = d N . The dielectric constant of the m t h layer is K m = K 1 + m N . For a very large N > 10 3 , the capacitance C is α K ∈ 0 A d l n 2 . The value of α will be____ [ ∈ 0 is the per
Correct answer
0
Step-by-step solution
Let m t h layer is at a distance ‘ x ’ from left plate. Also, let there be a small strip of thickness 'dx' having small capacitance ′ ′ d 1 C ′ ′ with medium ′ ′ K m ′ ′ in between. ⇒ x m = D N Also, d 1 C = d x K m ε 0 A = d x K m ε 0 A = d x K ε 0 A 1 + m N = d x K ε 0 A 1 + x D ⇒ 1 C e q = ∫ d 1 C = ∫ 0 D D d x K ε 0 A D + x 1 C e q = D K ε 0 A l n 2 C e q = K ε 0 A D l n 2 ⋅ Therefore α = 1