An electric motor has a 900 -turn coil on its armature. The...

An electric motor has a 900 -turn coil on its armature. The coil is circular with diameter $12 \mathrm{~cm}$ and carries 12.5 A. Find the maximum torque on the coil when it rotates in a 1.50 -T magnetic field.

Key Concepts

Area of a Circle

The area of a circle is a key geometric parameter in calculating the magnetic dipole moment of a circular coil. It is determined using the formula A = ?r², where r is the radius of the circle. For circular coils, the precise computation of the area is important since it directly influences the magnitude of the magnetic dipole moment and consequently the torque experienced in a magnetic field.

Magnetic Field

The magnetic field, measured in tesla (T), represents the intensity of the magnetic force in a given region. It influences the force acting on moving charges and current-carrying conductors, thereby playing a crucial role in the generation of torque on a current loop. The ability of a magnetic field to produce torque is harnessed in many practical applications, including electric motors.

Magnetic Dipole Moment

The magnetic dipole moment quantifies the strength and orientation of a current loop's magnetic effect. It is calculated by multiplying the number of turns, the current in the loop, and the area enclosed by the loop. This property is central to understanding how current loops interact with external magnetic fields, leading to a torque that can cause rotation.

Torque on a Current Loop

Torque on a current loop in a magnetic field arises due to the interaction between the magnetic dipole moment of the loop and the external magnetic field. The maximum torque occurs when the dipole moment is perpendicular to the magnetic field lines and is given by the product of the magnetic dipole moment and the magnetic field strength. This concept is fundamental in designing devices like electric motors.

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