A semicircular loop of radius r is placed on the axis of a current carrying circular ring of radius R ( R ≫ r ) , at a distance R 3 from the centre of the ring. The plane of the loop is making an an

Question

A semicircular loop of radius r is placed on the axis of a current carrying circular ring of radius R ( R ≫ r ) , at a distance R 3 ​ from the centre of the ring. The plane of the loop is making an angle of 5 3 ∘ with the plane of the ring. Find the coefficient of mutual induction between them :-

TestHub · Accepted Answer

Field on the ring axis at x = 3 ​ R : B = 2 ( R 2 + 3 R 2 ) 3/2 μ 0 ​ I R 2 ​ = 16 R μ 0 ​ I ​ . ϕ = B ⋅ 2 π r 2 ​ cos 5 3 ∘ = 16 R μ 0 ​ I ​ ⋅ 2 π r 2 ​ ⋅ 5 3 ​ . M = I ϕ ​ = 160 R 3 μ 0 ​ π r 2 ​ - option (B).

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