CLASS 12 PHYSICS · CHAPTER 5 · STUDY NOTES
Magnetism and Matter
An exploration of the universal nature of magnetism, the properties of bar magnets, Gauss's law for magnetism, and the classification of materials based on their magnetic response.
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Introduction to Magnetism
Explore attraction, repulsion and what changes when a magnet is cut.A north and south end face: the magnets attract. Attraction alone cannot prove both objects are magnets; unmagnetised iron can also be attracted. A freely suspended magnet aligns with the local field.
Picture from the NCERT book
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- Magnetic dipole
- A source with a magnetic moment. Cutting a bar magnet produces smaller magnets with paired north and south ends.
The north end of a freely suspended magnet follows the local magnetic field. Earth’s field usually gives a compass an approximately north–south orientation; it need not point exactly towards geographic north.
Like magnetic poles repel and unlike poles attract. Unmagnetised iron may also be attracted, so attraction alone does not establish that both objects are magnets.
Cutting across or along a bar gives smaller complete magnets. It does not isolate a pole. No isolated magnetic monopole has been experimentally established; the magnetic-field description used here has no sources or sinks of B.
Take a moment. What do you think?
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Question
Two objects attract. Does this prove both are permanent magnets?
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Magnetic Field Lines
Magnetic field lines provide a visual representation of the magnetic field's strength and direction in space.Outside the bar, B runs right to left from N to S; inside it returns from S to N. These curves are continuous and do not cross. The central arrow shows the return inside the magnet. A field line gives B, not the force on a moving charge. Curves approximate the external pattern; their count is not calibrated field strength.
- Field-line tangent
- The direction of B at a point. A compass’s north end follows this direction; the force on a moving charge generally does not.
| Property | Magnetic Field Lines | Electric Field Lines |
|---|---|---|
| Continuity | Form continuous closed loops | Discontinuous (start at +, end at -) |
| Intersection | Never intersect | Never intersect |
| Direction | Tangent gives direction of B | Tangent gives direction of E |
| Source | Magnetic dipoles (no monopoles) | Electric charges (monopoles exist) |
Around a bar magnet, field lines pass from N to S outside and return from S to N inside. They are continuous; the poles are not endpoints of B.
Within a consistently drawn field map, a higher line density indicates a stronger field. The number of curves in our schematic is illustrative, so do not use it as a numerical field measurement.
Lines cannot intersect at an ordinary point: a nonzero field vector has one direction there. Electric field lines instead start on positive charge and end on negative charge, or extend towards infinity.
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Question
Above the centre of the pictured bar, does the compass north end point towards N or towards S?
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Bar Magnet as an Equivalent Solenoid
A bar magnet and a current-carrying solenoid produce remarkably similar magnetic field patterns, suggesting they are fundamentally related.A coil with N = 100, I = 2 A and A = 10⁻³ m² has m = NIA = 0.20 A·m². A bar magnet with the same moment has the same leading far field. The microscopic current-loop analogy does not mean a magnet contains a literal wound wire. Reversing coil current exchanges its magnetic ends.
- Magnetic moment of a coil
- For N identical turns carrying current I and enclosing area A, m = NIA. Its direction follows the right-hand rule.
A finite solenoid has a field pattern resembling a bar magnet. Current direction determines which end behaves as N; reversing the current exchanges the ends.
At distances much larger than either source, equal magnetic moments give the same leading dipole field. On the axis B ≈ μ₀(2m)/(4πr³) along m. In the equatorial plane B ≈ μ₀m/(4πr³) opposite m.
At equal far distances the axial magnitude is twice the equatorial magnitude. Neither far-field expression should be used close to the bar or inside a solenoid. Microscopic magnetic moments include orbital and spin contributions; the current-loop analogy does not require literal wire coils inside matter.
An original coil example
m = NIAFor 120 turns, 0.50 A and 2.0 × 10⁻³ m² per turn, m = 120 × 0.50 × 0.0020 = 0.12 A·m². Reversing I reverses the moment while preserving its magnitude.
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Question
A far axial observation point is moved from r to 3r. What happens to B?
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The Dipole in a Uniform Magnetic Field
When a magnetic dipole, such as a needle or bar magnet, is placed in an external magnetic field, it experiences a torque that attempts to align it with the field.m = 0.40 A·m² and uniform B = 0.25 T. At θ = 60°, |τ| = mB sinθ = 0.087 N·m and U = −mB cosθ = -0.050 J. Zero energy is chosen at 90°. Turning quasistatically from 0° requires external work ΔU = 0.050 J. Torque is zero at both 0° and 180°; only 0° is a stable minimum. Net force is zero in this uniform field.
- Dipole potential energy
- U = −m·B = −mB cosθ, choosing U = 0 at θ = 90°. A constant may be added without changing the physics.
A dipole in a uniform external field experiences torque τ = m × B, with magnitude mB sinθ. Its net force is zero. A non-uniform field can also exert a net force.
The torque tends to align m with B. At 0° the energy is a stable minimum; at 180° it is an unstable maximum. Both positions have zero torque, so zero torque alone does not imply stability.
To turn the dipole slowly against the magnetic torque, an external agent does work equal to the rise in potential energy. From 0° to 90° the work is mB; from 0° to 180° it is 2mB.
Turning a needle slowly
W_external = ΔUA needle with m = 0.30 A·m² in B = 0.20 T is turned from 0° to 60°. U changes from −0.060 J to −0.030 J. The external work is +0.030 J; the field does −0.030 J.
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Question
The needle is exactly opposite B and its torque is zero. What happens after a tiny angular displacement?
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Gauss’s Law for Magnetism
Gauss's law for magnetism is a fundamental principle reflecting the absence of magnetic monopoles.Uniform B = 0.50 T passes through a box with end area 0.40 m². Outward normals give +0.20 Wb at the right face and −0.20 Wb at the left face. Four side faces contribute zero. Net closed-surface flux is 0 Wb, although each open end has nonzero flux.
- Gauss’s law for magnetism
- The signed magnetic flux through any closed surface is zero: ∮ B·dA = 0. The area vectors point outwards.
| Concept | Explanation |
|---|---|
| Electric Flux | Net flux exists if a net charge is enclosed; lines start/end on charges. |
| Magnetic Flux | Net flux is always zero; lines form closed loops; no monopoles. |
Flux through a small face is B·ΔA. A field leaving a closed volume contributes positive flux; a field entering contributes negative flux. The total cancels.
An open surface can have nonzero magnetic flux. Closing it adds the other faces and their signed contributions. Zero total flux does not mean B vanishes, or that every face has zero flux.
A surface surrounding one end of a bar also has zero net flux. The field returns through the magnet: the closed surface cannot contain an isolated pole simply by enclosing one visible end.
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Question
One face of a closed surface has +0.08 Wb and the other faces together have −0.08 Wb. Is the field necessarily zero inside?
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Magnetisation and Magnetic Intensity
To study the magnetic behavior of bulk matter, we define specific vector fields that distinguish between external influences and internal material responses.For a long solenoid, H = nI = 2000 A/m. This illustrative linear material has χ = -0.002, so M = χH = -4.0 A/m, μr = 0.998 and B = μ₀(H+M) = 2.508 mT. Negative M opposes H; positive M adds to it. B is measured in tesla; H and M in A/m. The linear core model does not describe ferromagnetic saturation or hysteresis.
- Magnetisation, M
- Net magnetic dipole moment per unit volume, M = m_net/V, measured in A/m.
- Magnetic susceptibility, χ
- For an isotropic linear material, M = χH. χ is dimensionless; negative χ means M opposes H.
Magnetic intensity H and magnetisation M have units A/m. Flux density B has units tesla. They satisfy B = μ₀(H + M); do not add quantities carrying different units.
For a long solenoid with negligible end effects, H = nI. A linear isotropic core gives B = μ₀(1 + χ)H, relative permeability μr = 1 + χ and permeability μ = μ₀μr.
Negative susceptibility slightly reduces B compared with the empty coil. Small positive susceptibility slightly increases it. Ferromagnetic materials generally have nonlinear, history-dependent responses; a single constant χ cannot describe saturation and hysteresis.
An original linear-core calculation
H = nI; M = χH; B = μ₀(H+M)Take n = 600 turns/m, I = 0.50 A and illustrative χ = 0.020. H = 300 A/m and M = 6 A/m. Using μ₀ ≈ 4π × 10⁻⁷ H/m gives B ≈ 0.385 mT.
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Question
A linear material has χ = −0.003. Is μr greater or less than one?
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Classification of Magnetic Materials
Materials are classified into three main categories—diamagnetic, paramagnetic, and ferromagnetic—based on their susceptibility and behavior in external fields.Without the applied field this sketch has no induced net moment. Diamagnets have χ < 0 and are weakly pushed towards lower B in a gradient. Water and bismuth are examples; the illustrated response is exaggerated.
- Magnetic domain
- A region of a ferromagnetic material in which atomic moments spontaneously share a common alignment.
- Remanence
- Magnetisation remaining after an applied magnetising field is removed. Its size depends on material and history.
| Property | Diamagnetic | Paramagnetic | Ferromagnetic |
|---|---|---|---|
| Susceptibility (χ) | Negative and small | Positive and small | Positive and large |
| Relative Permeability (μᵣ) | μᵣ < 1 | μᵣ > 1 | μᵣ > 1000 |
| Field Behavior | Expels field lines | Concentrates field lines | Highly concentrates lines |
| Examples | Water, Copper, Bismuth | Aluminium, Oxygen | Iron, Cobalt, Nickel |
Diamagnets develop an induced response opposite the applied field. Their small negative χ gives weak motion towards lower field in a gradient. Examples include water, copper and bismuth. Diamagnetism is present in all materials but may be masked by stronger effects.
Paramagnets have permanent atomic, ionic or molecular moments whose thermal orientations largely cancel without a field. An applied field creates a small average alignment along it. Aluminium and oxygen are examples. Stronger field or lower temperature can increase alignment, until saturation limits it.
Ferromagnetic domains already have internal alignment. Applying a field favours domains aligned with it; domain growth and rotation give a large bulk response. Hard magnetic materials retain more alignment than soft materials after the field is removed.
Above the Curie temperature, spontaneous ferromagnetic order disappears and the material becomes paramagnetic. The three categories describe the chapter’s main comparison, not every magnetic behaviour found in nature.
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Question
An unmagnetised piece of iron has no large net moment. Are the moments within each domain random?
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Superconductors and the Meissner Effect
Compare field penetration in the normal state with bulk exclusion in the Meissner state.Above the transition temperature the sample is normal; the applied field penetrates its bulk. Cool it into the Meissner state in a sufficiently weak field to compare. Zero electrical resistance and magnetic-flux expulsion are distinct properties.
- Meissner effect
- Exclusion of magnetic field from the bulk in the superconducting Meissner state, below the relevant critical temperature and field.
A superconducting state combines zero electrical resistance with a magnetic response. These are distinct properties: perfect conductivity alone is not a complete explanation of Meissner flux expulsion.
In the ideal bulk Meissner model, B = 0 and M = −H, so χ = −1 and μr = 0. A thin surface penetration layer is omitted. The measured response of a finite object also depends on its shape.
Complete exclusion needs sufficiently weak field and a temperature below the relevant transition. Type-II superconductors can admit magnetic vortices above a lower critical field while retaining superconductivity. Raising temperature or field far enough destroys the superconducting state.
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Question
Does “superconducting” guarantee zero B throughout a specimen for every applied field?
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Sign inNew here? Sign up freeNCERT reference: chapter PDF pages 13, 17.