A circular coil of radius 5.0 cm is wound with five turns...

A circular coil of radius 5.0 cm is wound with five turns and carries a current of 5.0 A. If the coil is placed in a uniform magnetic field of strength $5.0 \mathrm{T}$, what is the maximum torque on it?

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Key Concepts

Magnetic Moment

The magnetic moment of a current-carrying loop is a vector quantity that represents the strength and orientation of the magnetic source. It is calculated using the formula ? = NIA, where N is the number of turns, I is the current, and A is the area of the loop. The magnetic moment plays a crucial role in determining how the loop interacts with an external magnetic field.

Torque on a Current Loop

When a current loop is placed in a uniform magnetic field, it experiences a torque that tends to align the magnetic moment of the loop with the magnetic field direction. The torque is given by ? = ?B sin?, where ? is the angle between the magnetic moment and the magnetic field. The maximum torque occurs when sin? equals 1, meaning the magnetic moment is perpendicular to the magnetic field.

Uniform Magnetic Field

A uniform magnetic field is characterized by having the same magnitude and direction at every point in space. In problems involving magnetic torque on current loops, a uniform magnetic field simplifies calculations and is crucial for defining the constant interaction force on the magnetic moment of the loop.

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