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

step 1 Dear students, in problem 41 of chapter 19 we have asked that a square of a side 10 cm consists

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? (a) $0.96 \mathrm{~N}-\mathrm{m}$ (b) $2.06 \mathrm{~N}-\mathrm{m}$ (c) $0.23 \mathrm{~N}-\mathrm{m}$ (d) $1.36 \mathrm{~N}-\mathrm{m}$

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?
(a) $0.96 \mathrm{~N}-\mathrm{m}$
(b) $2.06 \mathrm{~N}-\mathrm{m}$
(c) $0.23 \mathrm{~N}-\mathrm{m}$
(d) $1.36 \mathrm{~N}-\mathrm{m}$

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Key Concepts

Torque on a Current Loop

The torque experienced by a current-carrying loop in a magnetic field is determined by the vector cross product of its magnetic dipole moment and the magnetic field. This torque tends to align the dipole moment with the field direction and is calculated using the formula ? = ?B sin?, where ? is the angle between the magnetic dipole moment and the magnetic field.

Magnetic Dipole Moment

The magnetic dipole moment is a measure of the strength and orientation of a current loop's magnetic field. It is calculated by the product of the current, the area of the coil, and the number of turns in the coil. In problems involving current loops, the dipole moment is used to quantify the torque experienced when placed in an external magnetic field.

Uniform Magnetic Field

A uniform magnetic field is one where the magnetic field strength and direction remain constant throughout the region of interest. In problems involving current loops, a uniform magnetic field simplifies calculations and ensures that the forces on each segment of the loop can be summed coherently to determine the net torque.

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