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. $\mathrm{A}$ horizontal magnetic field $B=6 \times 10^{-4} \mathrm{~T}$ 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 [Kerala CET 2009] (a) $2 \mathrm{~J}$ (b) $0.6\rfloor$ (c) $12 \mathrm{~J}$ (d) $6 \underline{1}$

A bar magnet having a magnetic moment of $2 \times 10^{4} \mathrm{JT}^{-1}$ is free to rotate in a horizontal plane. $\mathrm{A}$ horizontal magnetic field $B=6 \times 10^{-4} \mathrm{~T}$ 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 [Kerala CET 2009]
(a) $2 \mathrm{~J}$
(b) $0.6\rfloor$
(c) $12 \mathrm{~J}$
(d) $6 \underline{1}$

Key Concepts

Work Done by Changing Dipole Orientation

The work done in reorienting a magnetic dipole within a magnetic field is equal to the change in its potential energy between the two orientations. This concept underpins calculations involving the rotation of the dipole from one angle to another relative to the magnetic field direction.

Potential Energy of a Magnetic Dipole

The potential energy of a magnetic dipole in a magnetic field is given by the dot product of the magnetic moment and the magnetic field (with a negative sign). This energy quantifies how the alignment of the dipole with the field affects the system and is key to calculating work done during reorientation.

Magnetic Dipole

A magnetic dipole refers to any system that exhibits a north and south pole, characterized by a magnetic moment. It interacts with external magnetic fields, experiencing a torque that tends to align the dipole with the field direction.

Magnetic Moment

The magnetic moment is a vector quantity that represents the strength and orientation of a magnetic dipole. It determines the magnitude of the torque and energy interaction when the dipole is placed in a magnetic field.

Uniform Magnetic Field

A uniform magnetic field has the same magnitude and direction at every point in space. It exerts a consistent force on magnetic dipoles, leading to predictable torque and energy changes as the dipoles are rotated within the field.

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