Two short bar magnets of dipole moments M and M 3 are joined at right angles to form a cross as depicted in the figure. The value of θ for which the system remains in equilibrium in a uniform external magnetic field B

Correct answer: C. θ = 60 ° Torque (τ) acting on magnet (1), τ _ 1 = MBsin θ Similarly, τ _ 2 = 3 MBsin θ But for equilibrium, τ _ 1 = τ _ 2 ∴ MBsin θ = 3 MBcos θ tan θ = 3 = 60 ° ∴ θ = 60 °

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Physics
Chapter: Magnetic Properties of Matter

NTA Abhyas 2020 · Physics · Magnetic Properties of Matter

Two short bar magnets of dipole moments M and M 3 are joined at...

Two short bar magnets of dipole moments

M

and

M\sqrt{3}

are joined at right angles to form a cross as depicted in the figure. The value of

\theta

for which the system remains in equilibrium in a uniform external magnetic field

B

,& is

Two short bar magnets of dipole moments M and M 3 are joined at right angles to form a cross as depicted in the figure.

Options

A $\theta = 30 °$
B $\theta = 45 °$
C $\theta = 60 °$
D $\theta = 15 °$

Correct answer

C. $\theta = 60 °$

Step-by-step solution

Torque

\left(τ\right)

acting on magnet (1),

{τ}_{1} = MBsin \theta

Similarly,

{τ}_{2} = \sqrt{3}MBsin \theta

But for equilibrium,

{τ}_{1} = {τ}_{2}

∴ MBsin \theta = \sqrt{3}MBcos \theta

tan \theta = \sqrt{3} = \tan 60 °

∴ \theta = 60 °

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