A motor run by a 9.0-V battery has a 20 turn square coil...

A motor run by a $9.0-\mathrm{V}$ battery has a 20 turn square coil
with sides of length 5.0 $\mathrm{cm}$ and total resistance 24$\Omega .$ When
spinning, the magnetic field felt by the wire in the coil is
0.020 $\mathrm{T} .$ What is the maximum torque on the motor?

Key Concepts

Magnetic Torque on a Current Loop

This concept describes how a closed loop or coil carrying an electric current experiences a torque when subjected to an external magnetic field. The torque is due to the force acting on different segments of the current-carrying coil and is maximized when the plane of the coil is perpendicular to the magnetic field. The general expression involves the cross product of the coil's magnetic dipole moment with the magnetic field.

Magnetic Dipole Moment

The magnetic dipole moment is a measure of the strength and orientation of a magnet or a current loop. It is defined as the product of the current flowing through the loop and the area enclosed by it. This property directly affects the magnitude of the torque experienced by the coil in a magnetic field, making it a central concept in the analysis of electric motors.

Ohm's Law

Ohm's Law is a fundamental principle in electric circuits that relates the current, voltage, and resistance through the formula I = V/R. In the context of a motor, it is used to determine the amount of current flowing through the coil when a voltage is applied, which in turn influences the magnetic torque generated.

Coil Geometry and Area Calculation

The geometry of the coil, particularly the area enclosed by it, plays a critical role in determining its magnetic dipole moment. Accurate calculation of the area is essential, as it directly affects the resultant torque when the coil interacts with a magnetic field. This concept links the physical dimensions of the coil to its electromagnetic performance.

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