(a) A 200-turn circular loop of radius 50.0 cm is vertical,...

(a) A 200-turn circular loop of radius 50.0 cm is vertical, with its axis on an east-west line. A current of 100 A circulates clockwise in the loop when viewed from the east. Earth's field here is due north, parallel to the ground, with a strength of $3.0 \times 10^{-5} \mathrm{T}$. What are the direction and magnitude of the torque on the loop? (b) Does this device have any practical applications as a motor?

Key Concepts

Electromechanical Energy Conversion in Motors

The principle of converting electrical energy into mechanical energy in motors relies on the interaction between magnetic fields and current-carrying conductors. Understanding how a current loop experiences torque in a magnetic field is key to motor operation, though practical device applications also depend on factors like design efficiency, control mechanisms, and energy conversion effectiveness.

Right-Hand Rule

The right?hand rule is a fundamental tool in electromagnetism used to determine the direction of the magnetic dipole moment of a current loop and the resulting torque when placed in a magnetic field. By curling the fingers in the direction of the current flow, the thumb points in the direction of the associated magnetic moment, which is crucial when analyzing vector relationships in magnetic interactions.

Torque on a Magnetic Dipole

A magnetic dipole placed in a uniform magnetic field experiences a torque, which tends to align the dipole with the field. The magnitude and direction of this torque are given by the cross product of the dipole moment and the magnetic field, expressed as ? = ? × B. This explains how the interaction between the loop’s magnetic moment and the external magnetic field generates a rotational effect.

Magnetic Dipole Moment

The magnetic dipole moment is a vector quantity associated with a current loop that gives a measure of the loop’s ability to interact with a magnetic field. It is defined as the product of the current, the area of the loop, and the number of turns, with its direction determined by the right?hand rule. This concept is essential when analyzing the interaction of current loops with external magnetic fields.

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