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A magnetic needle initially aligned parallel to a magnetic field needs an amount of work equal to W to be rotated by 60°. The torque needed to hold the needle at this angular position is

1. 2W
2. W
3. W/√2
4. √3W

Correct answer: √3W

Solution

Work to rotate from 0 to 60 deg: W = MB(cos0 - cos60) = MB(1 - 0.5) = MB/2, so MB = 2W. Holding torque at 60 deg = MB*sin60 = 2W*(sqrt(3)/2) = sqrt(3)*W.

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