Two concentric rings are kept in the same plane. The number of turns in both the rings is 20. Their radii are 40 cm and 80 cm and they carry electric currents of 0.4 A and 0.6 A respectively, in mutually opposite directions. The magnitude of the magnetic field produced at their centre is T.

Question

Accepted Answer

(3) (10μ₀)/4. Given: coplanar concentric rings, N=20 turns each; R₁=0.4 m with I₁=0.4 A, R₂=0.8 m with I₂=0.6 A, the currents in opposite senses. Idea: at the centre of a coil of N turns, B=(μ₀NI)/(2R). Both fields are along the common axis, but opposite currents make them point opposite ways, so they subtract. Inner ring: B₁=(μ₀×20×0.4)/(2×0.4)=10μ₀. Outer ring: B₂=(μ₀×20×0.6)/(2×0.8)=7.5μ₀. Net field: B=10μ₀-7.5μ₀=2.5μ₀=(10μ₀)/4, about 3.14×10⁻⁶ T.

Two concentric rings are kept in the same plane. The number of turns in both the rings is 20. Their radii are 40 cm and 80 cm and they carry electric currents of 0.4 A and 0.6 A respectively, in mutually opposite directions. The magnitude of the magnetic field produced at their centre is ______ T.

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