Two similar coils each of radius R are lying concentrically with their planes at right angles to each other. The current flowing in them are I and 2I. The resultant magnetic field of induction at the

Question

Two similar coils each of radius R are lying concentrically with their planes at right angles to each other. The current flowing in them are I and 2I. The resultant magnetic field of induction at the centre will be ( μ 0 ​ = Permeability of vacuum)

TestHub · Accepted Answer

B 1 ​ = 2 R μ 0 ​ I ​ , B 2 ​ = 2 R μ 0 ​ ( 2 I ) ​ Resultant magnetic field, B = B 1 ​ + B 2 ​ ​ ∴ ∴ ∴ ​ B = ( 2 R μ 0 ​ I ​ ) 2 + ( 2 R μ 0 ​ ( 2 I ) ​ ) 2 ​ B = 2 R μ 0 ​ I ​ 1 2 + 2 2 ​ B = 2 R 5 ​ μ 0 ​ I ​ ​

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