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A magnetic needle initially aligned parallel to a uniform magnetic field is rotated by 60°. If the work done in this process is W, then the torque required to keep the needle fixed at this angle is

1. √(3)W
2. W
3. (√(3)/2)W
4. 2W

Correct answer: √(3)W

Solution

The torque required to maintain the needle at an angle in a magnetic field is proportional to the sine of the angle between the needle and the field. When the needle is rotated by 60°, the torque becomes sin(60°) times the work done, which results in ( rac{ ext{√3}}{2})W, leading to the conclusion that the torque is ext{√3}W.

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