JEE Main202125 Jul 2021Morning ShiftPhysicsCapacitanceActual
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 permittivity of the dielectric varies as: ε x = ε 0 + k x , for 0 < x ≤ d 2 ε x = ε 0 + k d - x , for d 2 ≤ x ≤ d
Options
- Aε 0 + k d 2 2 / k A
- Bk A 2 l n 2 ε 0 + k d 2 ε 0
- C0
- Dk A 2 ln 2 ε 0 2 ε 0 - k d
Correct answer
B. k A 2 l n 2 ε 0 + k d 2 ε 0
Step-by-step solution
Taking an element of width dx at a distance x x < d / 2 from left plate d c = ( ε 0 + k x ) A d x Capacitance of half of the capacitor 1 C = ∫ 0 d / 2 1 d c = 1   A ∫ 0 d / 2 d x ε 0 + k x 1 C = 1 k A l n ε 0 + k d / 2 ε 0 Capacitance of second half will be same C e q = C 2 = k A 2 l n 2 ε 0 + k d 2 ε 0