Diamagnetism

Hold a small chip of ordinary graphite or bismuth above a sufficiently strong magnet and, unlike an iron nail, it does not leap up to meet the pole — it drifts sideways, almost as if the magnet were faintly pushing it away. Nothing about the chip looks magnetic. It has no domains to line up, no compass-needle atoms waiting to swing into place. And yet every atom in it is quietly resisting the field, and that resistance is real enough to be measured, and in extreme laboratory demonstrations, strong enough to make a live frog float. This is diamagnetism — the faintest and strangest of the three magnetic personalities a material can show. Where a paramagnetic material has tiny permanent atomic magnets that a field can nudge into alignment, a diamagnetic atom starts with no net magnetic moment at all: its electrons are paired off, spin cancelling spin, orbit cancelling orbit. There is nothing for an external field to align. Instead, the field does something more subtle — it disturbs the electrons' own orbital motion just enough to create a brand-new, induced moment, and that induced moment always points backwards, opposing the very field that created it. The material is repelled not because it wants to escape the field, but because nature's induced response, like every induced response you have met since Lenz's law, opposes the change that caused it. This section asks three linked questions. What is the sign and typical size of a diamagnetic susceptibility, and why is it always negative? Where, physically, inside the atom, does the opposing moment come from? And why, unlike its paramagnetic and ferromagnetic cousins, does diamagnetism barely notice a change in temperature? Along the way we quantify the weak $M$ – $H$ – $\chi$ relationship with the same two numbers used in the board-level worked example, then push those numbers one step further to see just how astonishingly small the effect really is.

Key takeaways

Diamagnetism is universal but weak. Every material shows it, at the level of $\chi \sim -10^{-5}$ , but it is usually masked by stronger para- or ferromagnetic behaviour when those are present.
The susceptibility is small and negative: $\chi < 0$ , so the induced magnetisation $\vec M$ opposes the applied field $\vec H$ , and the relative permeability is very slightly below one, $\mu_r = 1+\chi \lesssim 1$ .
The origin is an induced atomic current, not a pre-existing dipole. Diamagnetic atoms have paired electrons whose moments already cancel; the field only induces a small extra circulation that opposes it — the atomic-scale echo of Lenz's law.
It is essentially temperature-independent, because there are no pre-existing dipoles for heat to disorder — unlike paramagnetism, which weakens sharply as a sample warms.
Behaviour in a non-uniform field is the classic identification test: a diamagnetic sample is pushed toward the weaker-field region and tends to orient perpendicular to $\vec B$ , the opposite of a paramagnetic sample.
Superconductors are the extreme case — perfect diamagnets with $\chi = -1$ , expelling the field from their interior almost entirely (the Meissner effect), though the deeper physics of superconductivity sits outside this syllabus.
Key idea: diamagnetism is a universal, weak, temperature-independent repulsion (χ < 0) caused by an induced atomic current opposing the applied field in materials whose electrons already have no net permanent moment.

The core insight

Diamagnetism is the small, negative-susceptibility, temperature-independent magnetic response of every material, arising because an applied field induces an opposing orbital current in atoms whose electrons are already paired and moment-free.

Where it fits in the syllabus

Diamagnetism is one of the three named classes of magnetic material in Unit V, Magnetism and Matter, of CBSE Class 12 Physics, alongside paramagnetism and ferromagnetism, and it sits under the prescribed sub-topic "magnetic properties of materials — dia-, para-, ferromagnetic substances with examples; magnetisation; effect of temperature on magnetic properties." You are expected to know the sign and rough size of $\chi$ , the qualitative atomic origin of the induced moment, representative examples, and the qualitative statement that diamagnetism barely changes with temperature — not a quantitative Curie-law treatment (that formal $\chi \propto 1/T$ relation is explicitly kept out of the 2025-26 syllabus, even for paramagnetism, and diamagnetism does not obey it in any case). The relations $M=\chi H$ , $\vec B=\mu_0(\vec H+\vec M)$ , and $\mu_r=1+\chi$ are standard, board-scope formulas used to describe magnetisation, not deep derivations you need to reproduce from first principles.

The physical picture

Every atom carries electrons in motion, and each moving electron is, from a magnetic point of view, a tiny current loop with its own magnetic moment. In most atoms these individual moments do not fully cancel, so the atom carries a small net permanent moment — the paramagnetic and ferromagnetic case. In a diamagnetic atom, by contrast, the electrons are arranged in pairs whose orbital and spin moments cancel exactly, so the atom, left alone, has zero net magnetic moment. Switch on an external field $\vec B$ , and something new happens: the field very slightly modifies each electron's orbital motion, adding a tiny extra circulating current on top of the existing orbit. By the same physical instinct you already trust from electromagnetic induction — an induced effect opposes the change that produces it — this extra circulation creates a small magnetic moment pointing opposite to the applied field. Multiply that tiny opposing moment by the enormous number of atoms in even a small sample, and you get a measurable, if very weak, bulk magnetisation opposing $\vec H$ . We describe this bulk response with the magnetic susceptibility $\chi$ , defined through

M = \chi H

where: $M$ is the magnitude of the magnetisation (magnetic moment per unit volume, in A/m) induced in the material, $H$ is the applied magnetic field intensity (A/m), and $\chi$ is the (dimensionless) magnetic susceptibility of the material. For a diamagnetic substance,

\chi < 0, \qquad |\chi| \sim 10^{-5} \text{ (typical order of magnitude)}

so $M$ always points opposite to $H$ , and the effect is tiny — a susceptibility of order $10^{-5}$ means the induced magnetisation is roughly a hundred-thousandth of the applied field intensity. The relative permeability, which tells you how the material modifies the total field compared with vacuum, follows directly:

\mu_r = 1+\chi \lesssim 1

where: $\mu_r$ is the relative permeability (dimensionless). For diamagnetic materials $\mu_r$ sits just under $1$ , meaning the material very slightly weakens the total magnetic field inside itself compared with the field that would exist there in vacuum. The picture below shows the two faces of the same idea: at the atomic scale, an induced current loop generates a moment opposing $\vec B$ ; at the bulk scale, the field lines inside a diamagnetic sample are very slightly excluded compared with the field outside.

Figure

An atomic view on the left showing an electron orbit with an induced current loop and a small magnetic moment arrow pointing opposite to the applied field, and a bulk view on the right showing external field lines slightly bending around a diamagnetic sphere while a few field lines pass through it more weakly than outside

Because every diamagnetic atom already has zero net moment before the field is switched on, there is no pre-existing atomic dipole for thermal agitation to disorder or realign. That is the physical reason diamagnetism, unlike paramagnetism, barely depends on temperature: the induced current mechanism runs on the electron's orbital response to the field itself, not on how well aligned a population of pre-existing dipoles happens to be at a given temperature.

Derivation AHow magnetisation weakens the field inside a diamagnetic material

The goal of this derivation is to connect the two quantities you actually measure or quote for a magnetic material — the susceptibility $\chi$ and the applied field intensity $H$ — to the total magnetic field $B$ that actually exists inside the material, using nothing beyond the definitions $M=\chi H$ and $\vec B=\mu_0(\vec H+\vec M)$ that are within syllabus scope; no atomic-level calculation of the induced current itself is required or expected, since that microscopic mechanism is explicitly qualitative-only in the prescribed scope.

Step 1. Start from the general relation between the total field, the applied field intensity, and the magnetisation that the material develops in response to it: $\vec B = \mu_0(\vec H+\vec M)$ . This says the field inside any magnetised material is the vacuum contribution from $H$ plus an extra contribution from whatever magnetisation the material itself has picked up.

Step 2. Substitute the defining relation for the material, $M=\chi H$ , into the expression from Step 1. Since $\vec M$ and $\vec H$ point along the same line for an isotropic material (parallel for $\chi>0$ , antiparallel for $\chi<0$ , which the sign of $\chi$ already carries), we can work with magnitudes: $B = \mu_0(H+\chi H) = \mu_0 H(1+\chi)$ .

Step 3. Identify the bracket as the relative permeability. Writing $\mu_r = 1+\chi$ , the result compresses to $B=\mu_0\mu_r H$ , which is the standard form relating the field inside a magnetic material to the applied field intensity through a single material constant, $\mu_r$ .

Step 4. Specialise to a diamagnetic material. Because $\chi<0$ for diamagnetic substances, $\mu_r=1+\chi$ is slightly less than $1$ , so $B=\mu_0\mu_r H$ is slightly less than the vacuum value $\mu_0 H$ — the field inside a diamagnetic sample is very slightly weaker than the field that would exist at the same point with the sample removed. Because $|\chi|\sim10^{-5}$ for an ordinary diamagnet, this weakening is minute; it becomes total exclusion, $\mu_r \to 0$ , only in the extreme limit $\chi \to -1$ , the perfect-diamagnet case realised by superconductors.

Worked examples

Board level - magnetisation from a given susceptibility

A diamagnetic sample has susceptibility $\chi = -6\times10^{-5}$ and is placed in a magnetic field intensity $H = 5\times10^{4}\ \text{A/m}$ . Find the magnetisation $M$ induced in the sample, and state its direction relative to $H$ .

Step 1. Write down the defining relation for a linear, isotropic magnetic material: $M=\chi H$ .

Step 2. Substitute the given values. $M = (-6\times10^{-5})\times(5\times10^{4}\ \text{A/m})$ .

Step 3. Evaluate the product. $M = -6\times5\times10^{-1}\ \text{A/m} = -3.0\times10^{0}\ \text{A/m}$ .

Step 4. Interpret the sign and state the answer. The negative sign shows that $\vec M$ points opposite to $\vec H$ , confirming diamagnetic behaviour. The induced magnetisation has magnitude $M = 3.0\ \text{A/m}$ , directed opposite to the applied field.

Competitive level - how much does the field inside actually change

Using the same sample ( $\chi=-6\times10^{-5}$ , $H=5\times10^{4}\ \text{A/m}$ ), find (a) the field $B_0$ that would exist at that point in vacuum, (b) the actual field $B$ inside the diamagnetic sample, and (c) the percentage change in the field caused by the material. Take $\mu_0=4\pi\times10^{-7}\ \text{T}\,\cdot\,\text{m/A}$ .

Step 1. Compute the vacuum field intensity's equivalent field, $B_0=\mu_0 H$ . $B_0 = (4\pi\times10^{-7})\times(5\times10^{4}) = 4\pi\times5\times10^{-3}\ \text{T} \approx 6.28\times10^{-2}\ \text{T}$ .

Step 2. Compute the relative permeability of the sample. $\mu_r = 1+\chi = 1-6\times10^{-5} = 0.99994$ .

Step 3. Compute the actual field inside the material using $B=\mu_0\mu_r H = \mu_r B_0$ . $B = 0.99994\times6.283\times10^{-2}\ \text{T} \approx 6.2826\times10^{-2}\ \text{T}$ , a reduction of only about $3.8\times10^{-6}\ \text{T}$ from $B_0$ .

Step 4. Express the change as a percentage. Since $B/B_0=\mu_r=1+\chi$ , the fractional change is exactly $\chi$ , so the percentage change is $\chi\times100\% = -6\times10^{-3}\ \%$ , i.e. the field inside is weaker by only about six-thousandths of one per cent. The vacuum-equivalent field is $B_0\approx 6.28\times10^{-2}\ \text{T}$ , the field inside the sample is $B\approx 6.2826\times10^{-2}\ \text{T}$ , and the material has shrunk the local field by roughly $0.006\%$ — a striking numerical demonstration of just how weak diamagnetism really is. Timing note: under two minutes. Notice the shortcut in Step 4 — you never need to subtract two nearly-equal large numbers to find the percentage change; $B/B_0=1+\chi$ means the fractional change is simply $\chi$ itself, read off instantly without further arithmetic. In an exam, quoting that shortcut is faster and safer than carrying five significant figures through a subtraction.

Common traps

Thinking diamagnetism only occurs in a handful of "special" materials — it is present, at some weak level, in every material, and is simply overwhelmed whenever stronger paramagnetic or ferromagnetic behaviour is also present.
Confusing diamagnetic repulsion with a permanent, pre-existing atomic magnetic moment — diamagnetism arises from an induced effect on paired-up, otherwise-cancelling electron motion, not from the alignment of dipoles that already existed.
Assuming diamagnetic susceptibility changes noticeably with temperature the way paramagnetic or ferromagnetic susceptibility does — it does not, to a good approximation, because there are no pre-existing dipoles for temperature to disorder.
Mixing up the direction rule — diamagnetic materials are repelled by, and move toward weaker regions of, a non-uniform field, and their $\chi$ is negative; do not accidentally apply the paramagnetic rule (attraction toward stronger field, positive $\chi$ ) to a diamagnetic sample.
Treating $\mu_r$ and $\chi$ as if they were far apart in size — for an ordinary diamagnet $\mu_r=1+\chi$ is only a whisker below $1$ , not some dramatically smaller number; students sometimes overstate how much the field actually changes.
Forgetting that superconductors are diamagnets taken to their extreme limit ( $\chi=-1$ , $\mu_r=0$ ) rather than a completely different phenomenon — the underlying sign and repulsion logic is the same, only the magnitude is different.

Common trapDiamagnetism is not "no magnetism" — it is the universal, weakest layer that every material has underneath whatever stronger behaviour is also present

The single biggest misconception is treating "diamagnetic" as a synonym for "non-magnetic." Every material — including the iron nail sitting on your desk — has an underlying diamagnetic response from its paired electrons; it is simply invisible in iron because the much stronger ferromagnetic response of its unpaired electrons dominates by many orders of magnitude. A material is called diamagnetic only when it has no stronger competing effect to hide behind. Similarly, do not assume the induced opposing moment means the material somehow "resists" the field's energy or violates any conservation law — it is an ordinary induced effect, entirely consistent with the field doing a tiny amount of work to set up the opposing atomic currents, exactly as Lenz's law would lead you to expect.

You should be able to…

State the sign and typical order of magnitude of $\chi$ for a diamagnetic material, and connect it to $\mu_r=1+\chi\lesssim1$ .
Explain, in your own words, the atomic-level origin of the induced diamagnetic moment, and why it requires electrons that are already paired.
Use $M=\chi H$ and $B=\mu_0(H+M)=\mu_0\mu_r H$ to compute magnetisation and the field inside a diamagnetic sample from given data.
Explain why diamagnetic susceptibility is essentially independent of temperature, in contrast with paramagnetic susceptibility.
Predict how a diamagnetic sample behaves in a non-uniform magnetic field (direction of force, orientation) and contrast it with a paramagnetic sample.
Recognise superconductors as the perfect-diamagnet limiting case ( $\chi=-1$ ) without needing to explain the mechanism of superconductivity itself.

Ask the tutor: Want a few more $M$ – $H$ – $\chi$ or $B$ -inside-the-material numericals built around diamagnetic samples, or a side-by-side comparison table against paramagnetism?

If diamagnetism is in every material, why do we not notice it in everyday objects?

Because it is extremely weak, with $\chi$ typically of order $10^{-5}$ , so the induced magnetisation is roughly a hundred-thousandth of the applied field intensity — far too small to feel with an ordinary magnet in daily life. It also gets completely swamped whenever a material has any stronger magnetic behaviour available, which is why we only call something diamagnetic when it has no unpaired electrons and no ferromagnetic domains competing for attention. Detecting it usually needs a very strong, carefully shaped non-uniform field and sensitive apparatus, which is why classroom demonstrations of diamagnetic levitation (even of small living things, in famous physics demonstrations) require electromagnets far stronger than an ordinary bar magnet.

Is water diamagnetic, and does that matter for anything in real life?

Yes — water is diamagnetic, which is precisely what makes the famous "floating frog" demonstration possible: in an extremely strong, carefully shaped magnetic field, the tiny diamagnetic repulsion acting on every water molecule in a small living creature (mostly water by mass) can be made to balance gravity. This is a genuine, published physics demonstration, not a trick, and it works purely because of the same $\chi<0$ , induced-current mechanism you have just studied, scaled up by an enormous applied field. It is a striking reminder that "weak" does not mean "negligible in every circumstance" — with a strong enough field, even a $10^{-5}$ -sized effect can lift something.

Why are superconductors described as perfect diamagnets, and is that in my syllabus?

A superconductor expels an applied magnetic field from its interior almost completely — the Meissner effect — which corresponds to $\chi=-1$ and $\mu_r=1+\chi=0$ in exactly the same $B=\mu_0\mu_r H$ framework you used in the worked examples, just pushed to its extreme limit. It is mentioned here only as a conceptual "what does the diamagnetic formula predict if $\chi$ becomes as negative as it can possibly be" example; the microscopic physics of superconductivity itself (Cooper pairs, critical temperature, and so on) is well beyond the CBSE Class 12 syllabus and is not something you need to derive or explain in an exam answer.

How is this different from what happens in a paramagnetic material — is it really just the opposite sign?

The sign flip ( $\chi<0$ versus $\chi>0$ ) is the visible symptom, but the underlying mechanism is genuinely different, not merely reversed. Paramagnetic atoms already possess a permanent net magnetic moment (from unpaired electrons) that a field merely aligns against thermal jostling, which is why paramagnetism weakens as temperature rises. Diamagnetic atoms have zero net moment to begin with — the field has to create the moment by disturbing orbital motion, a mechanism that does not depend on thermal alignment at all, which is exactly why diamagnetism stays essentially constant with temperature while paramagnetism does not.