Q1. A bar magnet of moment 0.4 A·m² is held at 30° to a uniform field of 0.2 T. Find the torque.
τ = mB sinθ
τ = 0.4 × 0.2 × sin30° = 0.4 × 0.2 × 0.5
τ = 0.04 N·m
Magnetism and Matter — Class 12
A bar magnet is just a magnetic dipole. Learn its torque in a field, the Earth as a giant magnet, and why materials respond differently to magnetism.
Magnetic dipole moment (m)For a current loop m = N·I·A; for a bar magnet it points from S to N. Unit: A·m². Torque in a field τ = mB sinθ.
Earth's magnetismEarth behaves like a giant bar magnet. Described by three elements: declination, inclination (dip) and the horizontal component of the field.
Dia-, Para- & FerromagnetismDiamagnetic (weakly repelled), paramagnetic (weakly attracted), ferromagnetic (strongly attracted, e.g. iron — can be permanently magnetized).
Magnetic intensity & magnetizationMagnetization M is the net dipole moment per unit volume; susceptibility χ = M/H tells how a material responds to a field H.
Dipole torque calculator Interactive
Find the maximum torque on a magnetic dipole placed perpendicular to a field (θ = 90°).
Max torque, τ = mB—N·m
Torque is maximum when the dipole is perpendicular to the field and zero when aligned with it.
Numericals practice Interactive
Dipole moment and torque problems with steps.
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Solved numericals
Q2. Give one difference between paramagnetic and diamagnetic substances.
Paramagnetic substances are weakly ATTRACTED by a magnet and move towards a stronger field.
Diamagnetic substances are weakly REPELLED and move towards a weaker field.
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Magnetic dipole moment | m = N I A | A·m² |
| Torque on a dipole | τ = m B sinθ | N·m |
| Potential energy of a dipole | U = − m B cosθ | J |
| Magnetic susceptibility | χ = M / H | — (no unit) |
Common mistakes & exam wins
- Torque on a dipole τ = mB sinθ is maximum at 90° and zero when aligned with the field.
- Ferromagnetic materials (iron, nickel, cobalt) can be permanently magnetized; they lose it above the Curie temperature.
- Earth's magnetic field is roughly that of a bar magnet tilted about 11° to its rotation axis.
- The magnetic field lines of a bar magnet form continuous closed loops (unlike electric field lines).
Frequently asked questions
What is a magnetic dipole moment?
A measure of the strength and orientation of a magnet or current loop; m = NIA for a loop, with unit A·m². It points from S to N of a magnet.
What are dia-, para- and ferromagnetic materials?
Diamagnetic materials are weakly repelled by a field; paramagnetic are weakly attracted; ferromagnetic (iron, etc.) are strongly attracted and can be permanently magnetized.
What is magnetic declination?
The angle between the geographic meridian (true north) and the magnetic meridian (compass north) at a place.
Why do magnetic field lines form closed loops?
Because isolated magnetic poles (monopoles) do not exist — every field line that leaves the north pole returns to the south pole through the magnet.