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Question:

Two coils 'P' and 'Q' are separated by some distance. When a current of 3 A flows through coil 'P', a magnetic flux of 10^-3 Wb passes through 'Q'. No current is passed through 'Q'. When no current passes through 'P' and a current of 2A passes through 'Q', the flux through 'P' is?

6.67× 10^-4 Wb

3.67× 10^-4 Wb

3.67× 10^-3 Wb

6.67× 10^-3 Wb

Solution:

Correct option is B. 6.67× 10^-4 Wb
Φ_q=μ_0i_1R^2/(2(R^2+x^2)^3/2)×π r^2=10^-3
Φ_p=μ_0i_2r^2/(2(r^2+x^2)^3/2)×π R^2
Φ_p/Φ_q=i_2/i_1
(r^2+x^2)^3/2/(R^2+x^2)^3/2=Φ_P/10^-3
2/3=Φ_P/10^-3
Φ_P=6.67× 10^-4.