मराठी
CUET (UG)
MCQ ऑनलाइन सराव परीक्षा१४८
संकल्पना स्पष्टीकरण६९२
अभ्यासक्रम

Torque on a Magnetic Dipole (Bar Magnet) in a Uniform Magnetic Field

Advertisements

Topics

Estimated time: 5 minutes
CISCE: Class 12

Introduction

A freely suspended bar magnet rotates when placed in a uniform magnetic field and finally comes to rest with its magnetic moment aligned along the field.

This turning effect is called torque.

Core idea: A magnetic field exerts a torque on a magnetic dipole, tending to align its magnetic dipole moment \[\vec m\] with the magnetic field \[\vec B\].

CISCE: Class 12

Derivation of Torque

Consider a bar magnet as N aligned current loops, each of area A, carrying current I.

For one current loop in a uniform magnetic field: τone loop = I A B sin⁡ θ

For N identical aligned loops:

τ = N (IAB sin⁡ θ)
τ = (NIA) B sin⁡ θ

For a magnetic dipole, m = NIA

Therefore, τ = m B sin⁡ θ

Vector form: \[\vec τ\] = \[\vec m\] × \[\vec B\]

Important: θ is always measured between \[\vec m\] and \[\vec B\].

CISCE: Class 12

Special Cases and Equilibrium

Orientation of \[\vec m\] relative to \[\vec m\] θ Torque Nature of position
Parallel 0° 0 Stable equilibrium
Perpendicular 90° Maximum: τmax = mB Maximum turning effect
Antiparallel 180° 0 Unstable equilibrium

Maximum torque

  • When θ = 90°, τmax ⁡= mB
  • Hence, m = \[\frac {τ_{max}}{⁡B}\]

Zero torque: τ = 0 when θ = 0° or 180°

SI Unit of Magnetic Dipole Moment:

m = \[\frac {τ}{B}\]​ = \[\frac {N m}{T}\]

Since 1 T = 1 N A−1m−1

[m] = A m2

Shaalaa.com | Matter and Magnetism part 6 (Dipole in Uniform Magnetic field -1)

Shaalaa.com


Next video


Shaalaa.com


Matter and Magnetism part 6 (Dipole in Uniform Magnetic field -1) [00:11:10]
S
Series: 1
0%


Matter and Magnetism part 6 (Dipole in Uniform Magnetic field -1)
00:11:10  undefined
Matter and Magnetism part 7 (Diapole in Uniform Magnetic field -2)
00:09:42  undefined
Matter and Magnetism part 8 (Diapole analogy of electrostatic vs magnetic)
00:03:44  undefined

Related QuestionsVIEW ALL [5]

A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is 60°, and one of the fields has a magnitude of 1.2 × 10–2 T. If the dipole comes to stable equilibrium at an angle of 15° with this field, what is the magnitude of the other field?

A bar magnet of magnetic moment 1.5 J T-1 lies aligned with the direction of a uniform magnetic field of 0.22 T.

What is the torque on the magnet in cases (i) and (ii)?

A rectangular loop of area 5m2, has 50 turns and carries a current of 1A. It is hold in a uniform magnetic field of 0.1T, at an angle of 30°. Calculate the torque experienced by the coil. 

A magnetic dipole of magnetic moment `0.72sqrt(2) "Am"^2` is placed horizontally with the north pole pointing towards east. Find the position of the neutral point if the horizontal component of the earth's magnetic field is 18 μT.

A bar magnet of magnetic moment 1.5 J T –1 lies aligned with the direction of a uniform magnetic field of 0.22 T.

  1. What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment:
    1. normal to the field direction,
    2. opposite to the field direction?
  2. What is the torque on the magnet in cases (i) and (ii)?
Advertisements
Share
Notifications

Englishहिंदीमराठी
Login
Create free account


      Forgot password?
Course
Use app×