📘 Magnetism and Matter
Physics • Class XII
Introduction to Magnetism
Magnetic phenomena are universal, affecting everything from galaxies to atoms. The Earth's magnetism predates human evolution. The term 'magnet' originates from Magnesia, Greece, where magnetic ore was discovered around 600 BC. Key historical figures in the study of magnetism include Oersted, Ampere, Biot, and Savart, who established that moving charges or electric currents produce magnetic fields. Key properties include: like magnetic poles repel each other, while unlike poles attract; cutting a bar magnet results in two smaller magnets; magnetic monopoles do not exist.
Basic Concepts of Magnetism
Key ideas regarding magnetism include: the Earth behaves as a magnet, with its magnetic field pointing from geographic south to north; a freely suspended bar magnet aligns itself in the north-south direction; similar poles repel each other, while opposite poles attract; magnets can be made from iron and its alloys.
Bar Magnet and Magnetic Field
The behavior of a bar magnet can be observed using iron filings on a glass sheet. The arrangement of filings reveals the two poles of the magnet. When freely suspended, the north pole points towards geographic north and the south pole towards geographic south. A bar magnet can be viewed as a collection of circulating currents, similar to a solenoid. Cutting a bar magnet in half results in two smaller magnets, each with weaker magnetic properties.
Magnetic Field Lines
Magnetic field lines can be plotted using the pattern of iron filings. They form continuous closed loops, unlike electric field lines which begin and end at charges. The tangent to a field line at any point indicates the direction of the net magnetic field (B) at that point. The density of field lines crossing a unit area indicates the strength of the magnetic field; more lines mean a stronger field. Magnetic field lines do not intersect, as this would imply multiple directions of the magnetic field at a single point. Magnetic field lines cannot emanate from a point and must always have a net flux of zero through any closed surface.
Magnetic Field of a Solenoid
The magnitude of the magnetic field (B) at point P due to a solenoid is given by the formula: B = (μ₀/4π) * (m/r³), where m is the magnetic moment and r is the distance from the solenoid. This formula also applies to the far axial magnetic field of a bar magnet.
Dipole in a Uniform Magnetic Field
When a small compass needle with a known magnetic moment (m) oscillates in a magnetic field (B), the torque (τ) on the needle is given by τ = m × B. The magnitude of the torque is τ = mB sin(θ), where θ is the angle between m and B. The magnetic potential energy (Uₘ) can be expressed as Uₘ = -m · B, with the zero of potential energy defined at θ = 90°.
Magnetic Potential Energy
The potential energy of a magnetic dipole in a magnetic field is defined by its orientation. It is minimum (–mB) at θ = 0° (most stable position) and maximum (+mB) at θ = 180° (most unstable position).
Magnetization and Magnetic Intensity
Magnetisation (M) is defined as the net magnetic moment per unit volume of a sample. It is a vector quantity with dimensions L⁻¹A and measured in A/m. In a long solenoid with n turns per unit length carrying a current I, the magnetic field inside is given by B₀ = μ₀nI. If the solenoid is filled with a material with non-zero magnetisation, the magnetic field inside is greater than B₀, expressed as B = B₀ + Bₘ, where Bₘ is the field contributed by the material core and is proportional to M (Bₘ = μ₀M).
Magnetic Relationships
The relationship between the total magnetic field B, magnetic intensity H, and magnetisation M is given by B = μ₀(H + M). The magnetic susceptibility χ is defined as χ = M/H. For paramagnetic materials, χ is small and positive; for diamagnetic materials, χ is small and negative, indicating that M and H are opposite in direction. The relative magnetic permeability (μᵣ) is defined as μᵣ = 1 + χ, and the magnetic permeability of the substance (μ) is given by μ = μ₀μᵣ.
Classification of Magnetic Materials
Materials can be classified based on their magnetic susceptibility (χ): Diamagnetic: χ is negative (-1 ≤ χ < 0); Paramagnetic: χ is positive and small (0 < χ < ε); Ferromagnetic: χ is large and positive (χ >> 1). The relative permeability (μr) also varies: Diamagnetic: 0 ≤ μr < 1; Paramagnetic: 1 < μr < 1 + ε; Ferromagnetic: μr >> 1.
Diamagnetism
Diamagnetic substances tend to move from stronger to weaker parts of an external magnetic field, exhibiting repulsion. The effect is usually weak, about one part in 10^5. Common diamagnetic materials include bismuth, copper, lead, silicon, nitrogen (at STP), water, and sodium chloride. Superconductors exhibit perfect diamagnetism, expelling all magnetic field lines, a phenomenon known as the Meissner effect.
Paramagnetism
Paramagnetic substances are weakly magnetised in an external magnetic field and tend to move from regions of weak to strong magnetic fields, indicating a weak attraction to magnets. This behavior is characterized by a positive susceptibility (χ > 0) but is generally much weaker than ferromagnetism.
Ferromagnetism
Ferromagnetic substances are strongly magnetized in an external magnetic field and are attracted to magnets. They have individual atoms with dipole moments that spontaneously align in a common direction over macroscopic volumes called domains. Common ferromagnetic elements include iron, cobalt, nickel, and gadolinium, with relative permeability greater than 1000.
Magnetic Moment and Torque
The magnetic moment (m) of a magnet is a vector quantity that determines the torque (τ) experienced by the magnet in a magnetic field (B). The torque can be calculated using the formula τ = m × B, where the angle between the magnetic moment and the magnetic field affects the magnitude of the torque.
Gauss's Law for Magnetism
Gauss's law for magnetism states that the net magnetic flux through any closed surface is zero. This can be expressed mathematically as: ∮ B · dS = 0, where B is the magnetic field and dS represents area elements.
Magnetic Field Calculations
The magnetic field H is calculated using the formula H = nI, where n is the number of turns per unit length and I is the current. The magnetic field B is derived from H using B = μr μ0 H. Magnetisation M is calculated as M = (B - μ0 H) / μ0.