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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 maximum


Formula used

U=-μ.B=μBcosθ(i), where U is the potential energy, μ is the magnetic moment and B the magnetic field.

τ=μBsinθ(ii), where τ is the torque.

Definitions

  1. Magnetic 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.
  2. 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.
  3. 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.

Solution

  1. From equations (i) and (ii) we can observe that potential energy will be zero when cosθ will be zero which will be at a value of 90°.
  2. And, at 90° sinθ is maximum that is one.
  3. This means in turn the torque will be maximum.

Hence, the correct answer is option (B).


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