A bar magnet having a magnetic moment of 2 ×10^4 JT^-1 is free to rotate in a horizontal plane.

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A bar magnet having a magnetic moment of 2 ×10^4 JT^-1 is...

A bar magnet having a magnetic moment of $2 \times 10^{4} \mathrm{JT}^{-1}$ is free to rotate in a horizontal plane. A horizontal magnetic field $\mathrm{B}=6 \times 10^{-4}$ Tesla exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction $60^{\circ}$ from the field is (a) $0.6 \mathrm{~J}$ (b) $12 \mathrm{~J}$ (c) $6 \mathrm{~J}$ (d) $2 \mathrm{~J}$

A bar magnet having a magnetic moment of $2 \times 10^{4} \mathrm{JT}^{-1}$ is free to rotate in a horizontal plane. A horizontal magnetic field $\mathrm{B}=6 \times 10^{-4}$ Tesla exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction $60^{\circ}$ from the field is
(a) $0.6 \mathrm{~J}$
(b) $12 \mathrm{~J}$
(c) $6 \mathrm{~J}$
(d) $2 \mathrm{~J}$

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Key Concepts

Magnetic Dipole Moment

This is a measure of the strength and orientation of a magnet's ability to produce a magnetic field. It plays a crucial role in determining the interaction energy between the magnet and an external magnetic field, and is fundamental to understanding magnetic dipoles in various physical systems.

Magnetic Potential Energy

A magnetic dipole in an external magnetic field has potential energy that depends on its orientation with respect to the field. This energy is given by the expression U = –m·B cos?, where m is the magnetic dipole moment, B is the magnetic field strength, and ? is the angle between the dipole moment and the magnetic field. This concept is key in analyzing the stability and dynamics of dipoles in magnetic fields.

Work Done in Reorienting a Magnetic Dipole

When a magnetic dipole rotates in a magnetic field, the work done is associated with the change in its potential energy. The work done in rotating the dipole from one orientation to another is found by calculating the difference in magnetic potential energy between the initial and final states. This principle is essential for solving problems involving energy changes due to rotational motion in a magnetic field.

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