Magnetism and Matter Class 12 Physics Formula Sheet 2026-27 | Important Formulas

CBSE Class 12 PhysicsChapter 52026–27Quick Revision

Magnetism and Matter Class 12 Physics — Formula Sheet + Quick Revision

A compact, syllabus-aware Magnetism and Matter Class 12 Physics formula sheet covering important formulas, magnetic dipole moment, torque, magnetic field lines, magnetic materials, magnetisation, magnetic susceptibility, permeability and exam traps for quick revision.

2026–27 syllabus boundary: Chapter 5 is part of Unit III, Magnetic Effects of Current and Magnetism, which carries 17 marks collectively with Chapter 4. The current CBSE syllabus covers the bar magnet and its qualitative equivalence to a solenoid; magnetic field intensity along and perpendicular to the dipole axis (qualitative); torque on a magnetic dipole in a uniform field (qualitative); magnetic field lines; dia-, para- and ferromagnetic substances; magnetisation; and temperature effects on magnetic properties. This page therefore separates current-scope revision from historical quantitative PYQ formulas.

How to use this page: Do not try to memorise every old textbook formula just because it appears in historical PYQs. For 2026–27, first master the qualitative ideas and relationships that are actually within the current syllabus. Use the PYQ page separately for historical question practice.

Formula-at-a-glance: m = NIA  |  τ = mB sinθ  |  M = magnetic moment/volume  |  χ = M/H  |  μ_r = 1 + χ.
For 2026–27, use the first three relationships as the core revision anchors; susceptibility/permeability are retained as conceptual relationships supported by CBSE learning outcomes.

1. Magnetic Dipole Moment

Current-carrying coil

m = NIA

m = magnetic dipole moment, N = number of turns, I = current, A = area of the coil. SI unit: A m².

Direction of magnetic moment

m → normal to the loop

Use the right-hand rule: curl fingers in the direction of current; the thumb gives the direction of m.

2. Torque on a Magnetic Dipole

Magnitude of torque

τ = mB sin θ

θ is the angle between magnetic dipole moment m and magnetic field B. The torque tends to rotate the dipole toward alignment with the field.

Maximum torque:
θ = 90° → τ_max = mB

Zero torque:
θ = 0° or 180° → τ = 0

Exam trap: Zero torque does not mean the two orientations are physically identical. Parallel and antiparallel orientations have different stability behaviour. Read the wording of the question carefully.

3. Magnetic Field of a Bar-Magnet Dipole — Current-Syllabus View

Important: The 2026–27 CBSE syllabus specifies the field along the axis and perpendicular to the axis qualitatively. Therefore, the conceptual comparison is more important than memorising a long derivation.

Position	What to remember	Revision cue
Axial position	Point lies on the magnetic dipole axis.	Think “along the axis”.
Equatorial position	Point lies on the perpendicular bisector/equatorial line of the dipole.	Think “perpendicular to the axis”.
Distance dependence	The ideal dipole field decreases as distance increases; the detailed inverse-cube relation belongs here only as historical quantitative practice.	For a current-scope qualitative question, explain the trend rather than forcing a derivation.

4. Historical Dipole-Field Relations — Use Only as Legacy PYQ Practice

Scope note: These relations are shown here only because historical board/PYQ material may contain quantitative dipole-field questions. They are not presented as a separate compulsory quantitative requirement of the current 2026–27 Chapter 5 syllabus.

Axial field of a short magnetic dipole

B_axial = (μ₀/4π)(2m/r³)

Historical quantitative relation. Use with the scope note above.

Equatorial field of a short magnetic dipole

B_equatorial = (μ₀/4π)(m/r³)

Magnitude relation for the ideal short-dipole model; direction is opposite to the dipole-moment direction on the equatorial line.

Useful historical comparison: at the same distance in the ideal short-dipole model, |B_axial| = 2|B_equatorial|.

Assessment-aware extension: The official CBSE Class XII 2026–27 Physics SQP includes an alternative 2-mark question on a material with relative permeability μ_r = 800 and an alternative on Gauss's law of magnetism. These are therefore useful revision items even though the current curriculum wording keeps the dipole-field treatment qualitative. Use them as assessment-aware extensions, not as a reason to expand the core syllabus unnecessarily.

5. High-Yield Extended Relations

Gauss's law for magnetism

∮ B · dA = 0

The net magnetic flux through any closed surface is zero. This is associated with the fact that magnetic field lines form closed loops rather than beginning or ending at isolated magnetic poles.

Magnetic field in matter

B = μ₀(H + M)

B is magnetic flux density, H is magnetic intensity and M is magnetisation.

Magnetisation relation

M = χH

For a linear magnetic material, magnetisation is proportional to magnetic intensity; χ is magnetic susceptibility.

Relative permeability

μ_r = 1 + χ

Useful for classification questions and directly relevant to the 2026–27 SQP's magnetic-material question.

Magnetic intensity

H = B/μ₀ − M

Rearranged from B = μ₀(H + M). SI unit of H: A m⁻¹.

Permeability

μ = μ₀μ_r = μ₀(1 + χ)

Use this with the material model being assumed. μ has SI unit T m A⁻¹ (equivalently N A⁻²).

Fast assessment cue: μ_r ≫ 1 → strong magnetic response, typically ferromagnetic in school-level classification. The official 2026–27 SQP uses μ_r = 800 as an example.

Optional reference — not a core 2026–27 requirement: Some older textbooks and PYQs use the magnetic-dipole potential-energy relation U = −mB cos θ. Keep it as background/reference knowledge rather than treating it as a compulsory current-syllabus formula.

6. Magnetic Field Lines — Fast Revision

Outside a bar magnet: field lines are conventionally drawn from N to S.

Inside a bar magnet: they continue from S to N, forming closed loops overall.

Field-line crossing: magnetic field lines do not intersect because that would imply two field directions at one point.

Field strength: closer field lines represent a stronger field qualitatively.

7. Dia-, Para- and Ferromagnetic Materials

Type	Response in an external field	Susceptibility χ	Typical examples
Diamagnetic	Weakly repelled by a magnetic field.	Small and negative.	Bismuth, copper, silver, water.
Paramagnetic	Weakly attracted by a magnetic field.	Small and positive.	Aluminium, platinum, oxygen.
Ferromagnetic	Strongly attracted; can show strong magnetisation.	Large and positive in the usual simplified comparison.	Iron, cobalt, nickel.

Do not confuse: “negative susceptibility” points to diamagnetic behaviour in the standard classification. “Positive susceptibility” can describe paramagnetic or ferromagnetic behaviour; the magnitude and material behaviour matter too.

8. Magnetisation

Definition

M = magnetic moment / volume

M is magnetisation, i.e. magnetic dipole moment per unit volume of the material. Dimensions: magnetic moment/volume; SI unit: A m⁻¹.

SI unit

A m⁻¹

Magnetisation is measured in ampere per metre.

9. Susceptibility and Permeability — Conceptual Revision

Magnetic susceptibility

χ = M/H

A dimensionless measure describing the magnetic response of a material to the magnetising field H. In the standard linear treatment, M = χH.

Relative permeability

μ_r = 1 + χ

Useful as a conceptual relationship in the usual linear-material treatment. Interpret it together with the material classification.

Material shortcut: χ < 0 → diamagnetic; χ small and positive → paramagnetic; ferromagnetic materials show a much stronger magnetic response and should not be reduced to a single “small χ” rule.

High-yield memory cues:

• Dia: weak repulsion, χ < 0.
• Para: weak attraction, χ small and positive.
• Ferro: strong attraction/ordering, strongly temperature-dependent.
• Magnetisation: magnetic moment per unit volume, SI unit A m⁻¹.

10. Temperature Effect on Magnetic Properties

Material	Temperature revision idea
Paramagnetic	Magnetic response generally decreases as temperature increases; thermal agitation opposes alignment.
Ferromagnetic	Increasing temperature weakens ferromagnetic ordering; above the Curie temperature, the material loses ferromagnetic behaviour and becomes paramagnetic in the standard model.
Diamagnetic	Diamagnetic response is comparatively weak and much less temperature-sensitive in the standard school-level treatment.

11. One-Minute Concept Map

Concept	Remember this
Bar magnet	Model it as a magnetic dipole.
Equivalent solenoid	Bar magnet can be understood qualitatively as equivalent to a current-carrying solenoid.
Magnetic moment	For a current loop: m = NIA.
Torque	τ = mB sinθ; maximum at 90°, zero at 0° and 180°.
Field lines	Closed loops; never intersect.
Diamagnetic	Weak repulsion; χ is negative.
Paramagnetic	Weak attraction; χ is small and positive.
Ferromagnetic	Strong magnetic response; temperature can destroy ferromagnetic ordering.
Magnetisation	M = magnetic moment per unit volume; SI unit A m⁻¹.

12. Common Exam Traps

• Trap 1: Do not confuse the direction of magnetic field lines outside a bar magnet (N → S) with the conventional direction of magnetic dipole moment (S → N).
• Trap 2: Do not call every positive-susceptibility material simply “paramagnetic”; ferromagnetic materials have a much stronger response.
• Trap 3: Diamagnetic means weakly repelled, not “completely unaffected”.
• Trap 4: Torque is zero at both θ = 0° and θ = 180°.
• Trap 5: Do not turn the current qualitative bar-magnet field treatment into an unnecessary derivation for a 2026–27 syllabus question.
• Trap 6: Unit III carries 17 marks collectively for Chapters 4 and 5; CBSE does not assign a fixed standalone 17 marks to Chapter 5.

13. 20-Minute Revision Sequence

1. 2 minutes — magnetic dipole and magnetic moment.
2. 3 minutes — torque and orientations.
3. 4 minutes — field lines and axial/equatorial qualitative picture.
4. 5 minutes — dia-, para- and ferromagnetic comparison.
5. 3 minutes — magnetisation, susceptibility and temperature effect.
6. 3 minutes — attempt selected Chapter 5 PYQs and check the traps above.

14. 60-Second Self-Check

• Can I state m = NIA and its SI unit?
• Can I identify when τ is maximum and zero?
• Can I distinguish axial and equatorial positions?
• Can I classify a material from the sign of χ?
• Can I explain why ferromagnetic behaviour weakens with increasing temperature?
• Can I state the current-syllabus boundary without importing obsolete quantitative requirements?

Continue Your Chapter 5 Preparation

Chapter 5 Notes Important Questions MCQs Numericals Case-Based Questions Assertion–Reason Previous Year Questions (PYQs) with Solutions

Link audit: All seven Learn Revise Hub Chapter 5 resource links below use the published canonical URLs supplied for this chapter. The two external links point to CBSE's official 2026–27 Physics curriculum and Class XII SQP/Marking Scheme portal. No placeholder or invented Chapter 5 URL is used on this page.

Official references: CBSE Physics Curriculum 2026–27 · CBSE Class XII 2026–27 SQP & Marking Scheme

Research note: This is an original revision resource, not an official CBSE document. The current syllabus boundary is based on the official CBSE 2026–27 Physics curriculum. Historical quantitative dipole-field relations are explicitly marked as legacy PYQ practice rather than current compulsory quantitative syllabus content.