An electric motor contains a 250 -turn circular coil 6.2 cm in diameter. If it develops a maximu

step 1 In this example, we are trying to find the magnetic field strength of a coil with 250 turns, a d

An electric motor contains a 250 -turn circular coil 6.2 cm...

An electric motor contains a 250 -turn circular coil $6.2 \mathrm{cm}$ in diameter. If it develops a maximum torque of $1.2 \mathrm{N} \cdot \mathrm{m}$ at a current of $3.3 \mathrm{A},$ what's the magnetic field strength?

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Key Concepts

Magnetic Field Strength

Magnetic field strength is a measure of the intensity of the magnetic field in which the coil is placed. It can be determined from the mechanical torque produced on the coil by using the relationship that connects torque, magnetic dipole moment, and magnetic field strength.

Magnetic Torque on a Current Loop

When a current-carrying loop is placed in a magnetic field, it experiences a torque. This torque is due to the interaction between the magnetic dipole moment of the loop and the applied magnetic field, and its magnitude depends on both the current through the loop and the area of the loop.

Magnetic Dipole Moment

The magnetic dipole moment is a measure of the strength of a magnetic source, and for a current-carrying coil it is given by the product of the current, the number of turns, and the area of the coil. This parameter is key in determining how the loop interacts with an external magnetic field.

Area of a Circular Coil

The area of a circular coil is important because it directly affects the magnetic dipole moment. It is calculated using the formula for the area of a circle, which relies on the coil's diameter or radius, linking the physical geometry of the coil with its electromagnetic properties.

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