Question

# Two magnets of equal mass are joined at right angles to each other, as shown in the figure. The magnet 1 has a magnetic moment four times that of magnet 2. This arrangement is pivoted so that it is free to rotate in the horizontal plane. In equilibrium, what will be the angle (θ) subtended by the magnet 1 with the magnetic meridian.

A
tan1(1)
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B
tan1(12)
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C
tan1(14)
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D
tan1(4)
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Solution

## The correct option is C tan−1(14) As per question, M1=4M2 ...(1) For the equilibrium of the system, torques on M1 and M2 should be of equal magnitude and in opposite direction. ⇒M1BHsinθ=M2BHsin(90∘−θ) ⇒tanθ=M2M1 ⇒tanθ=M24M2 [From (1)] ⇒tanθ=14 ⇒θ=tan−1(14) Hence, option (C) is the correct answer.

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