Class 12 Physics · Chapter 5 NotesMagnetism and Matter

A bar magnet has two poles, north and south, and when suspended freely it points approximately north-south. Like poles repel and unlike poles attract. Unlike electric charges, isolated magnetic poles (monopoles) do not exist; breaking a magnet gives two smaller magnets, each with both poles. The pattern of iron filings around a bar magnet reveals magnetic field lines. These lines form continuous closed loops, the tangent at any point gives the direction of the magnetic field B, and a larger density of lines means a stronger field. Field lines never intersect, because that would make the field direction ambiguous at the crossing point.

• Magnetic field lines are continuous closed loops.
• Tangent to a field line gives the direction of B.
• Closer field lines indicate a stronger magnetic field.
• Field lines never intersect.
• Magnetic monopoles do not exist.

The magnetic field lines of a bar magnet closely resemble those of a current-carrying solenoid. This suggests that a bar magnet can be thought of as a large number of circulating currents, in line with Ampere's hypothesis that all magnetic phenomena arise from circulating currents. Cutting a bar magnet in half is like cutting a solenoid, producing two smaller magnets. The axial field of a finite solenoid at a large distance r from its centre is B = (μ₀/4π)(2m/r³), which matches the far axial field of a bar magnet. Thus, a bar magnet and a solenoid produce similar magnetic fields, and the magnetic moment of a bar magnet equals that of an equivalent solenoid producing the same field.

• Bar magnet ≈ solenoid with circulating currents.
• Axial field at large distanceB = (μ₀/4π)(2m/r³).
• Magnetic moment of bar magnet equals that of equivalent solenoid.

When a small compass needle of magnetic moment m is placed in a uniform magnetic field B, it experiences a torque τ = m × B, with magnitude τ = mB sinθ, where θ is the angle between m and B. This torque tends to align the needle with the field. The magnetic potential energy is U = –m·B = –mB cosθ, taking the zero of energy at θ = 90°. The potential energy is minimum (–mB) at θ = 0°, the most stable orientation, and maximum (+mB) at θ = 180°, the most unstable orientation. In a uniform field, the net force on a dipole is zero, but a torque acts on it.

• Torqueτ = m × B, magnitude τ = mB sinθ.
• Potential energyU = –m·B = –mB cosθ.
• Stable equilibrium at θ = 0°, unstable at θ = 180°.
• Zero of potential energy chosen at θ = 90°.

The magnetic field of a bar magnet at large distances can be obtained from the electric dipole formulas by replacing E with B, p with m, and 1/ε₀ with μ₀. For a short bar magnet of magnetic moment m at distance r (r >> l), the equatorial field is B = –(μ₀/4π)(m/r³) and the axial field is B = (μ₀/4π)(2m/r³). Gauss's law of magnetism states that the net magnetic flux through any closed surface is zero: ∮ B·dS = 0. This reflects the absence of magnetic monopoles; magnetic field lines are continuous and form closed loops, with no sources or sinks.

• ReplacementsE → B, p → m, 1/ε₀ → μ₀.
• Equatorial fieldB = –(μ₀/4π)(m/r³).
• Axial fieldB = (μ₀/4π)(2m/r³).
• Gauss's law for magnetism∮ B·dS = 0.

Magnetisation M of a material is its net magnetic moment per unit volume: M = m_net / V, measured in A m⁻¹. When a material is placed in an external field, the total magnetic field inside is B = μ₀(H + M), where H is the magnetic intensity. For linear materials, M = χH, where χ is the magnetic susceptibility, a dimensionless quantity. The relative permeability is μ_r = 1 + χ, and the magnetic permeability is μ = μ₀μ_r. These three quantities are related, and only one is independent. Susceptibility is small and positive for paramagnetic materials, small and negative for diamagnetic materials, and large and positive for ferromagnetic materials.

• MagnetisationM = m_net / V (A m⁻¹).
• Magnetic intensityH = B/μ₀ – M.
• Total fieldB = μ₀(H + M).
• SusceptibilityM = χH.
• Relative permeabilityμ_r = 1 + χ; permeability: μ = μ₀μ_r.

Materials are classified as diamagnetic, paramagnetic or ferromagnetic based on their magnetic behaviour. Diamagnetic substances have a small negative susceptibility and are weakly repelled by magnets; they tend to move from stronger to weaker field regions. Examples include bismuth, copper, lead, silicon, nitrogen (at STP), water and sodium chloride. Paramagnetic substances have a small positive susceptibility and are weakly attracted to magnets; they move from weaker to stronger field regions. Examples include aluminium, sodium, calcium, oxygen (at STP) and copper chloride. Ferromagnetic substances have a large positive susceptibility and are strongly attracted to magnets; they can retain magnetisation and form permanent magnets. Examples include iron, cobalt, nickel and gadolinium.

• Diamagneticχ negative and small; weakly repelled.
• Paramagneticχ positive and small; weakly attracted.
• Ferromagneticχ large and positive; strongly attracted.
• Diamagnetism is present in all substances but often masked.

In ferromagnetic materials, atomic dipole moments interact cooperatively and align spontaneously over macroscopic regions called domains. A typical domain is about 1 mm in size and contains roughly 10¹¹ atoms. Initially, domains are randomly oriented, giving no net magnetisation. When an external field is applied, domains align with the field and grow in size, producing strong magnetisation. On removing the field, some materials retain magnetisation; these are hard ferromagnets, such as alnico and lodestone, used for permanent magnets. Others, like soft iron, lose magnetisation and are called soft ferromagnets. Ferromagnetism depends on temperature; above a certain temperature, a ferromagnet becomes paramagnetic as domain structure disintegrates.

• Domainsregions of spontaneous alignment, ~1 mm, ~10¹¹ atoms.
• Hard ferromagnets retain magnetisation (e.g., alnico, lodestone).
• Soft ferromagnets lose magnetisation (e.g., soft iron).
• Ferromagnetism disappears at high temperature.