A magnetie needle lying parallel to a magnetic field...

Name: Problem 3, Chapter 20: Master Resource Book in JEE Main Physics
Uploaded: 2022-01-14T15:18:27-08:00
Duration: 1 min 1 s
Channel: Narayan Hari
Description: A magnetie needle lying parallel to a magnetic field required W units of work to turn it through 60^∘ . The torque required to maintain the needle in this position will be (a) √(3) w (b) W (c) √(3) (W)/(2) (d) 2 W

A magnetie needle lying parallel to a magnetic field required $W$ units of work to turn it through $60^{\circ} .$ The torque required to maintain the needle in this position will be
(a) $\sqrt{3} w$
(b) $W$
(c) $\sqrt{3} \frac{W}{2}$
(d) $2 \mathrm{~W}$

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Key Concepts

Torque on a Magnetic Dipole

When a magnetic dipole is placed in a uniform magnetic field, it experiences a torque that tends to align the dipole with the field. This torque is proportional to the product of the dipole moment, the magnetic field strength, and the sine of the angle between the dipole moment and the magnetic field direction.

Rotational Work and Potential Energy

The work done in rotating a magnetic dipole in a magnetic field is stored as potential energy. The change in potential energy corresponds to the work required to rotate the dipole from one angular orientation to another, and this relationship is given by the integral of the torque over the angular displacement.

Magnetic Dipole Moment

This concept refers to a measure of the magnetic strength and orientation of a magnet or current loop. It is a vector quantity that interacts with external magnetic fields, and its magnitude determines the torque the dipole experiences when placed in a magnetic field.

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