A coil having 165 turns and a radius of 1.2 cm carries a current of 1.20 A. If it is placed in

step 1 Hi in the given problem number of turns in the coil is given as n is equal to 165 its radius is

A coil having 165 turns and a radius of 1.2 cm carries a...

A coil having 165 turns and a radius of $1.2 \mathrm{~cm}$ carries a current of $1.20 \mathrm{~A}$. If it is placed in a uniform $3.0 \mathrm{~T}$ magnetic field, find the torque this field exerts on the coil if the normal to the plane of the coil is oriented (a) perpendicular to the field, (b) parallel to the field, (c) at $30.0^{\circ}$ with the field.

Key Concepts

Magnetic Dipole Moment

The magnetic dipole moment is a measure of the strength and orientation of a magnetic source and is defined for a current-carrying loop as ? = NI A, where N is the number of turns, I is the current, and A is the area of the loop. It represents how the current loop interacts with external magnetic fields.

Torque on a Current Loop in a Magnetic Field

When a current loop is placed in a uniform magnetic field, it experiences a torque that tends to align its magnetic dipole moment with the magnetic field. This torque is given by ? = ?B sin ?, where B is the magnetic field strength and ? is the angle between the magnetic dipole moment and the magnetic field direction.

Area Calculation for a Circular Loop

For a current loop with a circular shape, the area A is calculated using the formula A = ?r², where r is the radius of the circle. This area is crucial in determining the magnetic dipole moment, as it relates the physical dimensions of the loop to its ability to interact with magnetic fields.

Dependence on Orientation Angle in Magnetic Torque

The magnitude of the torque on a current loop depends on the sine of the angle between the loop’s normal (which is aligned with the magnetic dipole moment) and the magnetic field. This dependence, expressed as sin ? in the torque equation, means that the torque is maximized when the angle is 90° and zero when the loop is aligned parallel to the field.

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