Question

A current loop in a magnetic field:

• A. can be in equilibrium in one orientation
• B. can be in equilibrium in two orientations, both the equilibrium states are unstable
• C. can be in equilibrium in two orientations, one is stable while the other is unstable
• D. experiences a torque where the field is uniform or non-uniform in all orientations.

Answer 1

The correct option is C

can be in equilibrium in two orientations, one is stable while the other is unstable

Explanation for the correct option

1. The interaction between the magnetic field lines of a magnet and the magnetic field produced by a current-carrying conductor causes a magnetic force on the conductor (as shown in the figure) which consequently produces torque on the conductor.
2. A current loop placed in a magnetic field experiences a torque ($\tau$) which is expressed by the below equation.
3. $\overrightarrow{\tau }=\stackrel{\rightharpoonup }{M}\times \overrightarrow{B}$
4. $\tau =MB\sin \theta$, where ($M$) is the magnetic moment of the loop, ($B$) is the magnetic field density and ($\theta$) is the angle between them.
5. $\theta =0^0\Rightarrow \sin 0^0=0\Rightarrow \tau =o$ and the current loop is said to be in a state of "stable equilibrium.
6. $\theta ={180}^0\Rightarrow \sin {180}^0=0\Rightarrow \tau =0$ and the current loop is said to be in a state of “unstable equilibrium”.
7. The potential energy ($U$) of the current loop is given by the equation, $U=-MB\cos \theta$
8. $\theta ={180}^0\Rightarrow \cos {180}^0=-1\Rightarrow U=+ve$
9. At ($\theta ={180}^0$), the potential energy of the current loop is maximum due to its orientation and the current loop is in the state of “unstable equilibrium”.
10. At ($\theta ={180}^0$), the torque acting on the current loop is ideally zero, however a slight push on the current loop will produce torque in the current loop.

Hence, option (C) is correct.