A magnetic needle is placed in a uniform magnetic field and is aligned with the field. The needle is now rotated by an angle of 60 degrees and work done is W. The torque on the magnetic needle at this position is

Explanation

The torque (τ) on a magnetic needle in a uniform magnetic field is given by the formula τ = mB sin(θ), where m is the magnetic moment, B is the magnetic field strength, and θ is the angle between the magnetic moment and the magnetic field. In this case, the needle is rotated by 60 degrees, so sin(60°) = √3/2. Therefore, the torque can be expressed in relation to the work done (W) when the needle aligns with the magnetic field. Since the work done is given as W, at 60 degrees, the correct torque value simplifies to √3 W. The other options are incorrect because they either miscalculate the sine value for the given angle or do not follow the relationship between torque and work accurately.