First slide

Magnetism

Question

M and $\sqrt{3}$ M are the magnetic dipole moments of two bar magnets which are joined to form a cross (+) structure. The combination is suspended freely in a uniform magnetic field . In the equilibrium position ,the angle between the bar magnet of magnetic moment M and the uniform magnetic field is

Moderate

A

$θ = 30 °$
B

$θ = 45^{0}$
C

$θ = 60^{0}$
D

$θ = 90 °$

Solution

Let the magnet having magnetic moment M makes an angle θ with the magnetic field.
Then, the magnet having magnetic moment $\sqrt{3}$ M makes an angle (90−θ) with the magnetic field. In equilibrium, both the torques are balanced.
$\begin{array}{l} MB \sin θ = \sqrt{3} MBsin (90 - θ) = \sqrt{3} MBcos θ \\ \Rightarrow \tan θ = \sqrt{3} = \tan 60^{\circ} \\ \Rightarrow θ = 60^{\circ} \end{array}$

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