Magnetism and Matter: common doubts, answered
The questions students ask most often about Magnetism and Matter, each with a short answer. For the full chapter, read the Magnetism and Matter notes.
About the chapter
How can I quickly tell diamagnetic, paramagnetic and ferromagnetic materials apart?
Look at the sign and size of χ. Diamagnets have small negative χ and μᵣ just below 1, and move towards weaker field. Paramagnets have small positive χ and μᵣ just above 1, and drift weakly towards stronger field. Ferromagnets have very large positive χ, with μᵣ that can exceed a thousand, and are pulled strongly towards strong field. Only ferromagnets can stay magnetised once the field is gone.
Magnets and their poles
Read this section in the notes →Why can't we get an isolated north pole by cutting a bar magnet?
Because each piece forms a fresh pair of poles where it is cut. Break a bar magnet in two and you get two smaller magnets, each with its own north and south pole, and this keeps happening however small the pieces become. No isolated magnetic pole, or monopole, has ever been found, which is why magnetism in matter is described in terms of dipoles.
Magnetic field lines
Read this section in the notes →Why do magnetic field lines form closed loops?
Because there are no magnetic monopoles for them to begin or end on. Outside a bar magnet the lines run from the north pole round to the south pole, and inside the magnet they continue from south back to north, closing every loop. Electric field lines are different: they start on positive charges and stop on negative ones.
Are magnetic field lines also lines of force?
No, not for a moving charge. The force on a moving charge is qv × B, which is perpendicular to B, so the charge is never pushed along a field line. The lines show the direction of B at each point, and their crowding shows its strength. This differs from electric field lines, whose tangent does give the direction of the force on a charge.
Bar magnet as an equivalent solenoid
Read this section in the notes →Why is a bar magnet said to be equivalent to a solenoid?
Because their fields away from the magnet have exactly the same form. A solenoid of N turns carrying current I, with cross-section A, has a magnetic moment m = NIA, and its far field matches that of a bar magnet of the same moment, both along the axis and on the equator. This supports the idea that a magnet's magnetism comes from tiny circulating currents inside it.
What is the SI unit of magnetic moment?
The SI unit of magnetic moment is A m², which is the same as J/T. The first form comes from m = NIA, current times area. The second follows from the energy U = −mB cos θ, which makes moment equal to energy divided by field. Both forms appear in questions, so recognise them as the same unit.
Dipole in a uniform field
Read this section in the notes →Why does a magnetic needle in a uniform field only rotate and not move?
Because a uniform field gives a torque but no net force. The two poles feel equal and opposite forces, which cancel as a total but form a couple. The torque τ = mB sin θ turns the needle until it lies along B. A needle pulled bodily towards a magnet is in a non-uniform field, such as near a pole, where the two ends feel different forces.
How much work is needed to turn a magnet from along the field to opposite to it?
It takes 2mB. The potential energy is U = −mB cos θ, which is −mB at 0° and +mB at 180°, so the work is the difference, mB − (−mB). Turning it only as far as 90° takes mB, because U is zero there. Remember that the zero of energy is at 90°, not when the magnet lies along the field.
Which position of a magnet in a uniform field is stable, and which is unstable?
Pointing along the field is stable; pointing opposite to it is unstable. At θ = 0° the energy −mB is the lowest possible, and a small tilt creates a torque that brings the magnet back. At θ = 180° the energy +mB is the highest. The torque there is also zero, but any small tilt grows, so the magnet swings round to the stable position.
The electrostatic analog
Read this section in the notes →What are the axial and equatorial fields of a short bar magnet?
At a distance r much larger than the magnet, the axial field is B_A = (μ₀/4π)(2m/r³), along m, and the equatorial field is B_E = −(μ₀/4π)(m/r³), opposite to m. So the axial field is twice the equatorial one at the same distance, and both fall as 1/r³. To recall them, take the electric dipole results and replace p with m and 1/4πε₀ with μ₀/4π.
Gauss's law for magnetism
Read this section in the notes →What does Gauss's law for magnetism say?
It says the net magnetic flux through any closed surface is always zero. Every field line that enters a closed surface must also leave it, since magnetic field lines are closed loops with no start or end. This is the formal statement that isolated magnetic poles do not exist. For electric fields, by contrast, the flux through a closed surface equals the enclosed charge divided by ε₀.
Magnetisation and magnetic intensity
Read this section in the notes →What is the difference between magnetic intensity H and magnetic field B?
H is set by the external currents, while B also includes the material's own response. They are linked by B = μ₀(H + M), where M is the magnetisation. In a solenoid H = nI, fixed by the winding alone. Slide an iron core in and H stays the same, but M becomes very large, so B rises enormously. H and M are measured in A m⁻¹, B in tesla.
How are relative permeability and magnetic susceptibility related?
They are related by μᵣ = 1 + χ, and μ = μ₀μᵣ = μ₀(1 + χ). Susceptibility χ = M/H tells how strongly a material magnetises; relative permeability compares B inside the material with B in vacuum for the same H. Both are dimensionless. A common slip is to write μᵣ = χ. For a diamagnet χ is small and negative, so μᵣ is a little below 1 but still positive.
Diamagnetism
Read this section in the notes →Why are diamagnetic substances repelled by a magnet?
Because the applied field induces a small magnetic moment opposite to itself, so M points against H and χ is negative. In such atoms the electron orbits have no net moment; the field speeds up some orbiting electrons and slows others, leaving a slight moment that opposes the field. A diamagnetic material therefore moves from stronger towards weaker field and pushes field lines slightly out of itself.
What is the Meissner effect?
It is the complete expulsion of magnetic field from the inside of a superconductor cooled below its transition temperature. The superconductor acts as a perfect diamagnet, with χ = −1 and μᵣ = 0. That is why a superconductor and a magnet repel each other strongly, and superconducting magnets can be used to levitate fast trains.
Paramagnetism
Read this section in the notes →Why do paramagnetic substances magnetise only weakly?
Because their atoms do have magnetic moments, but random thermal motion keeps scattering their directions. An applied field tends to line the moments up with it, giving a small positive χ and a weak pull towards stronger field. Only a small fraction lines up at ordinary temperatures; a stronger field or a lower temperature lines up more of them and raises the magnetisation.
Is copper paramagnetic or diamagnetic, and what about oxygen?
Copper is diamagnetic, and oxygen gas is paramagnetic. Other diamagnetic examples are bismuth, lead, silicon, water, sodium chloride and nitrogen; other paramagnetic ones are aluminium, sodium, calcium and copper chloride. Students often guess copper is attracted because it is a metal, but being a good conductor has nothing to do with being magnetic.
Ferromagnetism
Read this section in the notes →What are magnetic domains in a ferromagnet?
Domains are small regions, about a millimetre across, inside which the atomic moments are all lined up together. In an unmagnetised piece the domains point in random directions, so their moments cancel. An applied field turns the domains towards it and makes the already aligned ones grow at the expense of the rest, which is why a ferromagnet gains a very large magnetisation.
What is the difference between hard and soft ferromagnetic materials?
Hard ferromagnets stay magnetised after the field is removed, while soft ones lose their magnetisation. Alnico and naturally occurring lodestone are hard, so they make permanent magnets and compass needles. Soft iron loses its magnetisation easily, which suits uses where the magnetism must switch off or follow a changing current, such as electromagnets.
What happens to a ferromagnet when it is heated strongly?
It turns into a paramagnet. Heating breaks up the domain structure, and the magnetisation fades as the temperature rises until the spontaneous alignment is gone. The material then responds to a field only weakly, like any paramagnet. This is why strong heating can ruin a permanent magnet.
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