Concept understanding — Magnetic Materials Magnetization
From a Paperclip to a Magnet: The Intuition
You already know that a magnet can pick up iron nails. But what is actually happening inside that nail when it gets near the magnet? And why does a plastic comb, rubbed on hair, pick up tiny bits of paper — but never iron filings?
The answer lies in magnetization — the process by which a material becomes magnetic.
Think of a piece of iron as a chaotic crowd of tiny compass needles. Each needle is an atomic magnetic moment (a tiny magnet, arising from the spin of electrons). In unmagnetized iron, these needles point in random directions. Their magnetic effects cancel out, so the iron as a whole shows no net magnetism.
Now bring a strong magnet close. Its magnetic field acts like a command: "Line up!" The tiny compass needles inside the iron start rotating, aligning themselves with the external field. The more they align, the stronger the iron's own magnetic field becomes. This alignment is magnetization.
Note
Magnetization is not the same as inducing a current. It is a purely magnetic reorientation of atomic dipoles inside a material.
The Precise Definition
Magnetization (M) is the net magnetic dipole moment per unit volume of a material. It tells you how strongly a material is magnetized — how many tiny atomic magnets are aligned, and in which direction.
If a material has N atoms per unit volume, each with an average magnetic moment μavg, then:
M=Nμavg
The SI unit of M is amperes per metre (A/m). Why? Because a magnetic dipole moment has units of A·m², and dividing by volume (m³) gives A/m.
M=volumetotal magnetic dipole moment
How Magnetization Connects to the Magnetic Field
When a material gets magnetized, it produces its own magnetic field. The total magnetic field B inside the material is the sum of:
The external applied fieldH (caused by free currents, like the current in a solenoid)
The material's response — the magnetization M
The fundamental relation is:
B=μ0(H+M)
where μ0=4π×10−7T⋅m/A is the permeability of free space.
Watch out
Do not confuse H (magnetic field intensity, or "magnetizing field") with B (magnetic flux density). H is what you apply; M is what the material does; B is the total field you measure.
The Three Kinds of Magnetic Materials
Not all materials respond the same way to an external field. The magnetization M is proportional to H for most materials (at least for small fields):
M=χmH
where χm is the magnetic susceptibility — a dimensionless number that tells you how easily a material magnetizes.
Material Type
χm
Behaviour
Example
Diamagnetic
Small and negative (≈−10−5)
Weakly repelled by a magnet; M opposes H
Water, copper, bismuth
Paramagnetic
Small and positive (≈10−5 to 10−3)
Weakly attracted; M aligns with H
Aluminium, oxygen gas
Ferromagnetic
Large and positive (≫1)
Strongly attracted; M can be huge and persists even after H is removed
Iron, nickel, cobalt
Why this formula?
Magnetic Materials & Magnetization: Why the Key Formulas Hold
Let's build this from the ground up — starting with what magnetization physically means, then deriving the formulas step by step.
1. What is Magnetization (M)?
Magnetization is the net magnetic dipole moment per unit volume of a material.
Inside a material, atoms act like tiny magnetic dipoles (due to electron spin and orbital motion).
Without an external field, these dipoles point randomly → net M=0.
When an external field H is applied, dipoles align partially → net M=0.
Definition:
M=volumenet magnetic dipole moment
Units: A/m (same as H).
2. The Fundamental Relation: B=μ0(H+M)
This is the master equation linking the three magnetic fields:
B = magnetic flux density (the total field inside the material)
H = applied magnetic field (due to free currents)
M = magnetization (response of the material)
μ0 = permeability of free space (4π×10−7 H/m)
Why this form?
Step 1: In vacuum, there is no material, so M=0. Then:
B=μ0H
Step 2: Inside a material, the dipoles themselves produce an additional field. The total B is the sum of:
The field due to free currents (μ0H)
The field due to bound currents (from aligned dipoles), which is μ0M
Hence:
B=μ0H+μ0M=μ0(H+M)
Key insight:M is not an independent field — it's the material's response to H.
3. Magnetic Susceptibility (χm) and Permeability (μ)
For linear, isotropic, homogeneous materials (most common in exams), magnetization is proportional to the applied field:
M=χmH
χm = magnetic susceptibility (dimensionless)
χm>0 for paramagnetic materials
χm<0 for diamagnetic materials
χm≫1 for ferromagnetic materials (but not linear!)
Derivation of relative permeability μr:
Substitute M=χmH into the master equation:
B=μ0(H+χmH)=μ0(1+χm)H
Define:
μr=1+χm(relative permeability)
μ=μ0μr(absolute permeability)
Thus:
B=μH
Why this matters: It shows that the material simply scales the applied field by a factor μr.
4. Why χm Has Different Signs (Physical Reasoning)
Material Type
χm
Why?
Diamagnetic
χm<0 (small, ~10−5)
Applied field induces opposing dipole moments (Lenz's law at atomic level). M opposes H.
Paramagnetic
χm>0 (small, ~10−3)
Permanent atomic dipoles align partially with H. Thermal agitation fights alignment.
Both the electron and the proton are spin-21 particles, so each carries an intrinsic magnetic moment. But a spin moment scales inversely with the particle's mass through the charge-to-mass ratio, μ∝m1, and the proton is about 1836 times heavier than the electron.
Even after allowing for the proton's larger g-factor, its measured moment is only
A spin magnetic moment scales as μ∝1/m; the proton is ∼1836× heavier than the electron, so μp≈μB/660 — about 660 times smaller. Bulk magnetism is governed by electron moments, so the proton's contribution is negligible.
Why a spin moment depends on mass
Both particles have spin 21, so each has an intrinsic magnetic moment. For a particle of charge q, mass m and gyromagnetic factor g,
μ=g2mqS,S=2ℏ.
The two particles carry the same magnitude of charge, so the moment is controlled by the charge-to-mass ratio q/m — and hence by the mass.
Comparing proton and electron
The natural units are the Bohr and nuclear magnetons:
μB=2meeℏ,μN=2mpeℏ,μBμN=mpme≈18361.
The measured moments are μe≈μB (electron g≈2) and μp≈2.79μN (proton g≈5.6, from its composite structure). Therefore
μp≈2.79μN=18362.79μB≈660μB.
So even with the larger g-factor, the proton's moment is about 660 times smaller than the electron's.
Watch out
Equal spin quantum number does not mean equal magnetic moment. The moment depends on q/m, and the proton's much larger mass crushes it.
Method: Comparing Intrinsic (Spin) Magnetic Moments of Different Particles
Use this whenever a question asks you to compare or rank the magnetic-moment contribution of two different charged particles (e.g. electron vs. proton, or two different ions).
Steps
Step 1: Write the general spin magnetic-moment formula
Any spin-21 particle of charge q, mass m and gyromagnetic factor g has an intrinsic magnetic moment
μ=g2mqS,S=2ℏ.
This tells you immediately that μ depends on the particle only through g and the charge-to-mass ratio q/m — everything else (S) is common to every spin-21 particle.
Step 2: Isolate what actually differs between the two particles
If the two particles carry the same magnitude of charge (as electron and proton do), the comparison collapses to comparing g/m. Since g only varies by a factor of a few (electron g≈2, proton g≈5.6), while the mass ratio between an electron and a proton (or any nucleon) is enormous (mp/me≈1836), mass is the dominant factor — μ∝1/m.
Step 3: Use magneton units to make the comparison concrete
Express each moment in its natural unit — the Bohr magneton for the electron and the nuclear magneton for the nucleon: