A magnetic dipole of moment M is rotated slowly in a uniform magnetic field B from θ=30° to θ=120°, where θ is the angle between $\vec{M}$ and $\vec{B}$ .
The increase in its magnetic potential energy is:
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Question

A magnetic dipole of moment M is rotated slowly in a uniform magnetic field B from θ=30° to θ=120°, where θ is the angle between $\vec{M}$ and $\vec{B}$ .

The increase in its magnetic potential energy is:

Options

G1 Physics · Accepted Answer

Magnetic potential energy is U = -MB cosθ. Initially, U i U_i U i ​ = -MB cos30° = -(√3/2)MB. Finally, U f U_f U f ​ = -MB cos120° = +(1/2)MB. Therefore, ΔU = U f U_f U f ​ - U i U_i U i ​ = MB/2 + √3MB/2 = (√3+1)MB/2.

A magnetic dipole of moment M is rotated slowly in a uniform magnetic field B from θ=30° to θ=120°, where θ is the angle between M ⃗ \vec{M} M and B ⃗ \vec{B} B . The increase in its magnetic potential energy is: