    Question

# A magnetic dipole in a constant magnetic field has

A

zero potential energy when the torque is minimum

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B

zero potential energy when the torque is maximum

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C

minimum potential energy when the torque is maximum

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D

maximum potential energy when the torque is maximum

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Solution

## The correct option is B zero potential energy when the torque is maximumFormula used$U=-\stackrel{\to }{\mu }.\stackrel{\to }{B}=\mu B\mathrm{cos}\left(\theta \right)\dots \left(i\right)$, where $U$ is the potential energy, $\mu$ is the magnetic moment and $B$ the magnetic field.$\tau =\mu B\mathrm{sin}\left(\theta \right)\dots \left(ii\right)$, where $\tau$ is the torque.DefinitionsMagnetic dipole: A magnetic dipole is the limit of a closed system of electric current or a pair of poles when the size of the source is decreased to zero while the magnetic moment remains constant in electromagnetism.Torque in the magnetic field: The normal vector of a current loop strives to align with the magnetic field when it is subjected to a magnetic field. This is called torque. Potential Energy in the magnetic field: The amount of work required to rotate a magnetic dipole from zero potential energy to any desired location is defined as the potential energy of the dipole in a magnetic field. In a magnetic field, a current loop does not feel a net force. It, on the other hand, is subjected to torque.SolutionFrom equations (i) and (ii) we can observe that potential energy will be zero when $\mathrm{cos}\left(\theta \right)$ will be zero which will be at a value of $90°$. And, at $90°$ $\mathrm{sin}\left(\theta \right)$ is maximum that is one. This means in turn the torque will be maximum.Hence, the correct answer is option (B).  Suggest Corrections  0      Similar questions  Explore more