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

A motor run by a 9.0-V battery has a 20-turn square coil with sides of length 5.0 cm and total resistance 28 $\Omega$. When spinning, the magnetic field felt by the wire in the coil is 0.020 T. What is the maximum torque on the motor?

Key Concepts

Circuit Current Calculation

Using Ohm's law, current in the circuit is calculated as I = V/R, where V represents the battery voltage and R is the total resistance of the coil. This calculation is crucial because the current determines the strength of the magnetic dipole moment of the loop, which directly affects the resulting torque in the magnetic field.

Area of the Coil

The area of the coil (A) is fundamental to determining the magnetic dipole moment and thus the torque on the coil in a magnetic field. For regularly shaped coils like a square, the area is computed using the geometry of the coil (for example, side length squared in a square). This area measurement provides the scale over which the magnetic force acts to produce a torque.

Magnetic Torque on a Current Loop

This concept explains that a current-carrying loop placed in a magnetic field experiences a torque. The torque is given by the formula ? = N · I · A · B · sin?, where N is the number of turns in the coil, I is the current, A is the area of the loop, B is the magnetic field strength, and ? is the angle between the normal to the loop and the magnetic field. Maximum torque is achieved when sin? equals 1, meaning the loop is oriented such that its plane is perpendicular to the magnetic field.

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