Two magnets are suspended by a given wire one by one. In order to deflect the first magnet through 4 5 ∘ , the wire has to be twisted through 54 0 ∘ whereas with the second magnet, the wire requires a

Question

Two magnets are suspended by a given wire one by one. In order to deflect the first magnet through 4 5 ∘ , the wire has to be twisted through 54 0 ∘ whereas with the second magnet, the wire requires a twist of 36 0 ∘ for the same deflection. Then the ratio of magnetic moments of the two magnets is

TestHub · Accepted Answer

If C is torque per unit angular twist of the wire, then for a twist ϕ , τ = Cϕ = MB sin θ . In the 1 st case, ϕ 1 ​ = 54 0 ∘ − 4 5 ∘ = 49 5 ∘ , θ 1 ​ = 4 5 ∘ In the 2 nd case, ϕ 2 ​ = 36 0 ∘ − 4 5 ∘ = 31 5 ∘ , θ 2 ​ = 4 5 ∘ Dividing (i) by (ii), we get M 2 ​ M 1 ​ ​ = 315 495 ​ = 7 11 ​

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