A magnet of magnetic moment 50 ↑A m^2 is placed along the X -axis in a mag. field B^-=(0.5 ↑+3.0

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A magnet of magnetic moment 50 ↑A m^2 is placed along the X...

A magnet of magnetic moment $50 \uparrow \mathrm{A} \mathrm{m}^{2}$ is placed along the $\mathrm{X}$ -axis in a mag. field $\mathrm{B}^{-}=(0.5 \uparrow+3.0 \mathrm{~J} \wedge$ ) Tesla. The torque acting on the magnet is N.m. (c) $75 \mathrm{k} \wedge$ (d) $25 \sqrt{5} \mathrm{k} \wedge$ (a) $175 \mathrm{k}$ (b) $150 \mathrm{k}$

A magnet of magnetic moment $50 \uparrow \mathrm{A} \mathrm{m}^{2}$ is placed along the $\mathrm{X}$ -axis in a mag. field $\mathrm{B}^{-}=(0.5 \uparrow+3.0 \mathrm{~J} \wedge$ ) Tesla. The torque acting on the magnet is
N.m.
(c) $75 \mathrm{k} \wedge$
(d) $25 \sqrt{5} \mathrm{k} \wedge$
(a) $175 \mathrm{k}$
(b) $150 \mathrm{k}$

Key Concepts

Magnetic Moment

A magnetic moment is a vector quantity that represents the strength and orientation of a magnet or current loop. It quantifies how a magnetic object interacts with an external magnetic field, playing a central role in determining the torque and energy when placed in such a field.

Magnetic Field

A magnetic field is a vector field that exerts a force on moving charges and magnetic dipoles across space. Its properties include both magnitude and direction at any point and are critical in analyzing how magnetic forces and torques are applied to objects with magnetic moments.

Torque on a Magnetic Dipole

The torque experienced by a magnetic dipole in a magnetic field arises as the result of the vector cross product between the magnetic moment and the magnetic field. This torque tends to rotate the dipole so that its magnetic moment aligns with the applied field, and its magnitude is given by the product of the magnitudes of the two vectors and the sine of the angle between them.

Vector Cross Product

The vector cross product is an operation on two vectors that results in another vector perpendicular to the plane defined by the original vectors. Its magnitude is calculated as the product of the magnitudes of the original vectors multiplied by the sine of the angle between them, which is crucial in determining the torque produced by a magnetic dipole in a magnetic field.

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