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Physics-

General

Easy

Question

Two magnets of equal mass are joined at right angles to each other as shown the magnet 1 has a magnetic moment 3 times that of magnet 2. This arrangement is pivoted so that it is free to rotate in the horizontal plane. In equilibrium what angle will the magnet 1 subtend with the magnetic meridian

$\tan^{- 1} (\frac{1}{2})$
$\tan^{- 1} (\frac{1}{3})$
$\tan^{- 1} (1)$
0°

The correct answer is: $tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator 3 end fraction close parentheses$

For equilibrium of the system torques on M₁ and M₂ due to B_H must counter balance each other i.e. $M subscript 1 end subscript cross times B subscript H end subscript equals M subscript 2 end subscript cross times B subscript H end subscript$ . If q is the angle between M₁ and B_H will be $left parenthesis 90 minus theta right parenthesis$ ; so $M subscript 1 end subscript B subscript H end subscript sin invisible function application theta equals M subscript 2 end subscript B subscript H end subscript sin invisible function application left parenthesis 90 minus theta right parenthesis$
$rightwards double arrow tan invisible function application theta equals fraction numerator M subscript 2 end subscript over denominator M subscript 1 end subscript end fraction equals fraction numerator M over denominator 3 M end fraction equals fraction numerator 1 over denominator 3 end fraction rightwards double arrow theta equals tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator 3 end fraction close parentheses$

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