The intrinsic magnetic dipole moment of the electron has...

The intrinsic magnetic dipole moment of the electron has magnitude $9.3 \times 10^{-24} \mathrm{A} \cdot \mathrm{m}^{2} .$ What is the maximum torque on an electron due to its intrinsic dipole moment in a $1.0 \mathrm{T}$ magnetic field?

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Key Concepts

Magnetic Dipole Moment

The magnetic dipole moment is a vector quantity that represents the strength and orientation of a magnetic source, such as an electron. It quantifies how much the electron behaves like a tiny bar magnet, and its magnitude is used to calculate the interaction energy and torque when placed in an external magnetic field.

Magnetic Field

A magnetic field is a vector field that describes the magnetic influence exerted by magnets, currents, or other magnetic dipoles. It exerts forces on moving charges and magnetic dipoles, and its strength and direction are key factors in calculating physical effects such as torque.

Torque on a Magnetic Dipole

The torque experienced by a magnetic dipole in a magnetic field results from the tendency of the dipole to align with the field. This torque is mathematically expressed as the cross product of the magnetic dipole moment and the magnetic field, with its magnitude given by ? = ?B sin?, where ? is the angle between the two vectors.

Angular Dependence of Magnetic Torque

The torque on a magnetic dipole is dependent on the sine of the angle between the dipole moment and the magnetic field. The maximum torque occurs when this angle is 90 degrees, meaning the dipole is perpendicular to the field, leading to maximal rotational effect as it tries to align with the magnetic field.

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