Published by:
CGP EDU Academic Team
Published on: September 12, 2026
If a bar magnet of magnetic moment M is freely suspended in a uniform magnetic field of strength B , the work done in rotating the magnet through an angle
is
Text Solution
Verified by ExpertsThe correct answer is:
D
Step 1: The potential energy (U) of a magnetic dipole in a magnetic field is given by the formula:
U = - extbf{M} ullet extbf{B} = -MB ext{cos}( heta).
Step 2: The work done (W) in rotating the dipole from an angle of 0 to theta is the change in potential energy.
Step 3: When the angle changes from 0 to \theta, we calculate the change in potential energy:
W = U_{ ext{final}} - U_{ ext{initial}} = ig(-MB ext{cos}( heta)ig) - ig(-MB ext{cos}(0)ig)
W = -MB ext{cos}( heta) + MB = MB(1 - ext{cos}( heta)).
Thus, the work done in rotating the magnet through an angle \theta is given by W = MB(1 - ext{cos}(\theta)).
Therefore, option D is the correct answer.
U = - extbf{M} ullet extbf{B} = -MB ext{cos}( heta).
Step 2: The work done (W) in rotating the dipole from an angle of 0 to theta is the change in potential energy.
Step 3: When the angle changes from 0 to \theta, we calculate the change in potential energy:
W = U_{ ext{final}} - U_{ ext{initial}} = ig(-MB ext{cos}( heta)ig) - ig(-MB ext{cos}(0)ig)
W = -MB ext{cos}( heta) + MB = MB(1 - ext{cos}( heta)).
Thus, the work done in rotating the magnet through an angle \theta is given by W = MB(1 - ext{cos}(\theta)).
Therefore, option D is the correct answer.
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