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Question

When a D.M. is set in tanA position, the deflection is 30o for a magnet A placed at a distance of 40 cm from the midpoint of the D.M. When the D.M. is kept in tanB position another magnet B produces a deflection of 60o, when placed at the same distance. The ratio of the magnetic moments of A and B is :

A
1:2
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B
1:3
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C
2:3
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D
1:6
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Solution

The correct option is D 1:6
The deflection off the magnetic needle in tan A position by a short magnet is given by
μo4π2MAd3=BHtanθA
The deflection off the magnetic needle in tan B position by a short magnet is given by
μo4πMBd3=BHtanθB
tanθAtanθB=2MAMB
MAMB=12×tan30tan60=16

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