First slide

Magnetism

Question

A magnet is suspended in the magnetic meridian with un twisted wire. The upper end of the wire is rotated through $180^{0}$ to deflect the magnet by $30^{0}$ from magnetic meridian. Now this magnet is replaced by another magnet. Now the upper end of the wire is rotated through $270^{0}$ to deflect the magnet $30^{0}$ from the magnetic meridian. The ratio of the magnetic moments of the two magnets is

Moderate

A

3:4
B

1:2
C

4:7
D

5:8

Solution

During equilibrium, Torsional torque should be balanced by magnetic torque.
$C (α - θ) = M B \sin θ$
Where C is the couple per unit deflection & $α$ is the twisted angle, $θ$ is the deflection angle
Given : $α_{1} = 180 °, θ = 30 °, α_{2} = 270 °$
for first magnet $C (180 - 30) = M_{1} B \sin 30 °$
for second magnet $C (270 - 30) = M_{2} B \sin 30$
Dividing, $\frac{150}{240} = \frac{M_{1}}{M_{2}} = \frac{5}{8}$

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