Question

The torque and magnetic potential energy of a magnetic dipole in most stable position in a uniform magnetic field of magnetic strength $5\text{T}$, having magnetic moment $\mu =2{\text{Am}}^2$ will be

• A. $10\text{N-m},+20\text{J}$
• B. $20\text{N-m},-10\text{J}$
• C. $0\text{N-m},-10\text{J}$
• D. $0\text{N-m},+10\text{J}$

Answer 1

The correct option is C $0\text{N-m},-10\text{J}$

Given,
magnetic field strength, $B=5\text{T}$,

magnetic moment, $\mu =2{\text{Am}}^2$,

Torque of a magnetic dipole, $$\overrightarrow{\tau }=\overrightarrow{\mu }\times \overrightarrow{B}$$$\Rightarrow \tau =\mu B\sin \theta$

And magnetic potential energy, $$U=-\overrightarrow{\mu }.\overrightarrow{B}=-\mu B\cos \theta$$Magnetic dipole remains in most stable position when its magnetic potential energy is minimum, i.e, when the magnetic field vector is parallel to the magnetic moment vector.

So, at $\theta =0^{\circ }$, the dipole will be in its most stable position.

$\Rightarrow \tau =\mu B\sin 0^{\circ }=0$

$\Rightarrow U=-\mu B\cos 0^{\circ }=-2\times 5=-10\text{J}$

Hence, option (c) is the correct answer.