Question

# A current loop in a magnetic field:

A

can be in equilibrium in one orientation

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B

can be in equilibrium in two orientations, both the equilibrium states are unstable

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C

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

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D

experiences a torque where the field is uniform or non-uniform in all orientations.

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Solution

## The correct option is C can be in equilibrium in two orientations, one is stable while the other is unstableExplanation for the correct optionThe 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.A current loop placed in a magnetic field experiences a torque ($\tau$) which is expressed by the below equation.$\stackrel{\to }{\tau }=\stackrel{⇀}{M}×\stackrel{\to }{B}$$\tau =MB\mathrm{sin}\theta$, where ($M$) is the magnetic moment of the loop, ($B$) is the magnetic field density and ($\theta$) is the angle between them.$\theta ={0}^{0}⇒\mathrm{sin}{0}^{0}=0⇒\tau =o$ and the current loop is said to be in a state of "stable equilibrium.$\theta ={180}^{0}⇒\mathrm{sin}{180}^{0}=0⇒\tau =0$ and the current loop is said to be in a state of “unstable equilibrium”.The potential energy ($U$) of the current loop is given by the equation, $U=-MB\mathrm{cos}\theta$$\theta ={180}^{0}⇒\mathrm{cos}{180}^{0}=-1⇒U=+ve$At ($\theta ={180}^{0}$), the potential energy of the current loop is maximum due to its orientation and the current loop is in the state of “unstable equilibrium”.At ($\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.

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