A rectangular loop consists of 100 closely wrapped turns and...

A rectangular loop consists of 100 closely wrapped turns and has dimensions $0.40 \mathrm{~m}$ by $0.30 \mathrm{~m}$. The loop is hinged along the $y$ -axis, and the plane of the coil makes an angle of $30.0^{\circ}$ with the $x$ -axis (Fig. P19.28, page 658 ). What is the magnitude of the torque exerted on the loop by a uniform magnetic field of $0.80 \mathrm{~T}$ directed along the $x$ -axis when the current in the windings has a value of $1.2 \mathrm{~A}$ in

Key Concepts

Torque on a Magnetic Dipole

When a magnetic dipole is placed in a uniform magnetic field, it experiences a torque that tends to rotate it to align with the field. This torque is given by the cross product of the dipole moment and the magnetic field (? = ? × B), with a magnitude of ? = ?B sin?, where ? is the angle between the dipole moment and the magnetic field direction.

Uniform Magnetic Field

A uniform magnetic field is characterized by having the same magnitude and direction at every point in space. This uniformity allows for simplified calculations of forces and torques on current-carrying loops, as each segment of the loop experiences the same magnetic influence.

Magnetic Dipole Moment

This concept describes the vector quantity associated with a current loop that quantifies its ability to interact with a magnetic field. It is defined as the product of the number of turns, the current in the winding, and the area enclosed by the loop (? = NIA). The dipole moment points perpendicular to the plane of the loop, following the right-hand rule.

Loop Geometry and Area

In applications involving magnetic dipole moments, the geometry of the current loop is essential because the area of the loop directly influences the magnitude of the dipole moment. For example, in a rectangular loop, the area is calculated as the product of its length and width, which must be taken into account along with the number of turns and the current to determine the overall magnetic response.

Transcript

Please give Ace some feedback