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Physics Question on Magnetic Effects of Current and Magnetism

A magnetic dipole aligned parallel to a uniform magnetic field requires a work of W units to rotate it through 60°. The torque exerted by the field on the dipole in this new position is:

A

2W

B

W

C

23​​W

D

3​W

Answer

23​​W

Explanation

Solution

 The torque τ on a magnetic dipole in a magnetic field is given by:\text{ The torque } \tau \text{ on a magnetic dipole in a magnetic field is given by:}\\\\
τ=MBsin⁡θ\tau = M B \sin \theta
where M is the magnetic moment, B is the magnetic field, and θ is the angle between the dipole and the field.\text{where } M \text{ is the magnetic moment, } B \text{ is the magnetic field, and } \theta \text{ is the angle between the dipole and the field.}\\\\
Given that the angle θ=60∘, the torque becomes:\text{Given that the angle } \theta = 60^\circ, \text{ the torque becomes:}\\\\
τ=MBsin⁡60∘=MB×32\tau = M B \sin 60^\circ = M B \times \frac{\sqrt{3}}{2}
Thus, the torque is 32W, which corresponds to option 3.\text{Thus, the torque is } \frac{\sqrt{3}}{2} W, \text{ which corresponds to option 3.}