A coil with magnetic moment 1.45 A · m ^ 2 is oriented initially with its magnetic moment an

step 1 This is Chapter 27, Problem Number 46. We have a coil with a magnetic moment antiparralral to th

A coil with magnetic moment 1.45 A · m ^ 2 is oriented...

A coil with magnetic moment 1.45$\mathrm { A } \cdot \mathrm { m } ^ { 2 }$ is oriented initially with its magnetic moment antiparallel to a uniform $0.835 - \mathrm { T }$ magnetic field. What is the change in potential energy of the coil when it is rotated $180 ^ { \circ }$ so that its magnetic moment is parallel to the field?

A coil with magnetic moment 1.45$\mathrm { A } \cdot \mathrm { m } ^ { 2 }$ is oriented initially with its magnetic moment antiparallel to a uniform $0.835 - \mathrm { T }$
magnetic field. What is the change in potential energy of the coil
when it is rotated $180 ^ { \circ }$ so that its magnetic moment is parallel to
the field?

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Key Concepts

Magnetic Moment

The magnetic moment is a vector that characterizes the strength and orientation of a magnetic source, such as a current-carrying coil. It determines how the object interacts with an external magnetic field, affecting the forces and torques exerted on it.

Magnetic Field

A magnetic field is a vector field that exerts influence on moving charges and magnetic dipoles. It is defined by its magnitude and direction, and it governs the potential energy and dynamics of magnetic objects placed within it.

Magnetic Potential Energy

Magnetic potential energy is the energy associated with the orientation of a magnetic dipole in a magnetic field. It is given by the expression U = -? · B, where the energy depends on the cosine of the angle between the magnetic moment and the field, reflecting how rotation alters the system’s energy.

Torque on a Magnetic Dipole

A magnetic dipole in a magnetic field experiences a torque given by ? = ? × B, which tends to rotate the dipole so as to align it with the field. This torque is responsible for the work done on the dipole as it rotates, thereby changing its potential energy.

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