A square coil of side 10 cm consists of 20 turns and carries a current of 12 A . The coil is s

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A square coil of side 10 cm consists of 20 turns and...

A square coil of side $10 \mathrm{~cm}$ consists of 20 turns and carries a current of $12 \mathrm{~A} .$ The coil is suspended vertically and the normal to the plane of the coil makes an angle of $30^{\circ}$ with the direction of a uniform horizontal magnetic field of magnitude $0.80 \mathrm{~T}$. What is the magnitude of torque experienced by the coil?

Key Concepts

Magnetic Dipole Moment

This is a measure of the strength and orientation of a current loop’s magnetic character. It is calculated as the product of the current, the number of turns in the coil, and the area enclosed by the loop. The magnetic dipole moment is key to determining the magnetic effects of a current-carrying coil in a magnetic field.

Torque on a Magnetic Dipole

This concept explains the tendency of a current loop (or magnetic dipole) to rotate when placed in a magnetic field. The torque is given by the cross product of the magnetic dipole moment and the magnetic field vector, with its magnitude determined by the product of the dipole moment, the magnetic field strength, and the sine of the angle between them.

Uniform Magnetic Field

A uniform magnetic field is one where the magnetic field strength and direction are constant throughout the region of interest. In problems involving current loops, a uniform magnetic field simplifies the analysis by ensuring that each segment of the loop is subjected to the same magnetic influence.

Area of a Coil

The area of a coil is essential in calculating its magnetic dipole moment, and consequently, the torque it experiences in a magnetic field. For a coil of a given geometric shape, such as a square, the area is determined by the dimensions of the shape, which directly impacts the overall magnetic response of the coil.

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