(a) What is the maximum torque delivered by an electric...

(a) What is the maximum torque delivered by an electric motor if it has 80 turns of wire wrapped on a rectangular coil of dimensions $2.50 \mathrm{~cm}$ by $4.00 \mathrm{~cm}$ ? Assume that the motor uses $10.0 \mathrm{~A}$ of current and that a uniform $0.800$ -T magnetic field exists within the motor. (b) If the motor rotates at $3600 \mathrm{rev} / \mathrm{min}$, what is the peak power produced by the motor?

(a) What is the maximum torque delivered by an electric motor if it has 80 turns of wire wrapped on a rectangular coil of dimensions $2.50 \mathrm{~cm}$ by $4.00 \mathrm{~cm}$ ? Assume that the motor uses $10.0 \mathrm{~A}$ of current and that a uniform $0.800$ -T magnetic field exists within the motor.
(b) If the motor rotates at $3600 \mathrm{rev} / \mathrm{min}$, what is the peak power produced by the motor?

Key Concepts

Magnetic Dipole Moment

This concept refers to the measure of the strength and orientation of a magnetic source, such as a current-carrying loop. In an electric motor, the dipole moment is determined by the number of turns, the current flowing, and the area of the loop. It fundamentally characterizes how the loop interacts with an external magnetic field.

Torque on a Current Loop

When a current loop is placed in a magnetic field, it experiences a torque that tends to align the magnetic dipole moment with the field. The torque is given by the product of the magnetic dipole moment and the magnetic field strength, and it reaches its maximum value when the plane of the loop is perpendicular to the magnetic field. This principle is central to the operation of electric motors.

Rotational Kinematics

This area deals with the motion of objects rotating about an axis, including the conversion between rotational rate units (such as revolutions per minute to radians per second). Understanding these conversions is essential for analyzing rotational motion and determining quantities like angular velocity, which are used to compute mechanical power in rotating systems.

Peak Mechanical Power in Rotational Systems

Peak mechanical power represents the maximum rate at which work is done in a rotating system. It is usually calculated as the product of the maximum torque and the angular velocity. This concept is important in assessing the performance of devices like electric motors, where torque and rotation speed directly affect power output.

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