Suppose a circular coil and a conductor are kept adjacent to each other in same plane. Calculate the mutual inductance if the radius of circular coil is 'r' with 'n' number of turns kept at distance 'l' from the conductor.

Asked by Topperlearning User | 7th Jul, 2015, 11:36: AM

Expert Answer:

Consider a circular coil and a conductor are kept adjacent to each other in same plane.

Let, r  be the radius of circular coil and 'n' be the number of turns kept at distance 'l' from the conductor.

Mutual inductance is given as,

begin mathsize 12px style straight M equals straight ϕ over straight I end style

begin mathsize 12px style straight ϕ equals magnetic space flux space linked space with space all space the space turns space of space the space adjacent space coil
straight ϕ equals nBA
straight ϕ equals straight n open parentheses fraction numerator straight mu subscript 0 straight I over denominator 2 πd end fraction close parentheses open parentheses πr squared close parentheses
straight M equals fraction numerator straight n open parentheses fraction numerator straight mu subscript 0 straight I over denominator 2 πd end fraction close parentheses open parentheses πr squared close parentheses over denominator straight I end fraction
rightwards double arrow straight M equals straight n open parentheses fraction numerator straight mu subscript 0 over denominator 2 πd end fraction close parentheses open parentheses πr squared close parentheses end style

Answered by  | 7th Jul, 2015, 01:36: PM