THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Magnetic domain
A microscopic region inside a ferromagnet in which all atomic moments point in the same direction. Bulk ferromagnets are partitioned into many such domains, averaging to zero or near-zero net magnetization at rest.
Magnetic energy density
The energy stored per unit volume of a magnetic field: u_B = B²/(2μ₀) in vacuum, u_B = ½ BH in linear matter. The magnetic counterpart of the electric field energy density ε₀E²/2.
Magnetic field
The vector field B that exerts a sideways force on moving charges and steady currents. Sourced by currents and intrinsic spin, never by isolated magnetic charges.
Magnetic moment
The vector m = IA n̂ that quantifies the strength and orientation of a magnetic dipole. Determines its torque, energy, and far-field structure in any external field.
Magnetic monopole
A hypothetical particle carrying isolated magnetic charge g, sourcing the dual field tensor *F^{μν} the way an electron sources F^{μν}. Predicted in 1931 by Dirac as quantum-mechanically consistent; force charge quantisation; arise naturally in grand-unified theories. Never observed despite sixty years of dedicated search.
Magnetic permeability
The factor μ that relates B to H in a linear magnetic material: B = μH. Vacuum has μ = μ₀; other materials are characterised by the relative permeability μ_r = μ/μ₀ = 1 + χ.
Magnetic susceptibility
The dimensionless ratio χ = M/H measuring how strongly a linear magnetic material is magnetised by an applied H-field. Negative for diamagnets, positive and small for paramagnets, large for ferromagnets.
Magnetization
The vector M = (magnetic dipole moment)/(volume) inside a magnetised material, measured in amperes per metre. The magnetic analogue of polarization density.
Malus's law
I = I₀ cos²θ. The transmitted intensity of linearly polarised light through an ideal polariser depends on the cosine-squared of the angle between the incident polarisation and the polariser's transmission axis.
Manifold
An n-dimensional space that locally looks Euclidean. Each point has a neighbourhood homeomorphic to ℝⁿ; a *smooth* manifold adds a differentiable structure compatible across overlapping coordinate patches. A sphere is a 2-manifold; spacetime in general relativity is a 4-manifold.
mass
The quantitative measure of a body's inertia; the m in F = ma.
Mass-energy equivalence
Einstein's 1905 result E = mc² — that mass and energy are the same physical quantity expressed in different units, with c² as the conversion factor. Binding energies and kinetic energies register on a balance as mass; the foundation of nuclear physics, fusion, fission, and particle production.
Maxwell stress tensor
T_ij = ε₀(E_iE_j − ½δ_ij E²) + (1/μ₀)(B_iB_j − ½δ_ij B²). The 3×3 symmetric tensor whose divergence gives the mechanical force per unit volume the electromagnetic field exerts on charges and currents.
Maxwell's equations
The four coupled partial differential equations (∇·E = ρ/ε₀, ∇·B = 0, ∇×E = −∂B/∂t, ∇×B = μ₀J + μ₀ε₀ ∂E/∂t) that fully describe classical electromagnetism. Every electromagnetic phenomenon below the quantum scale follows from them.
Metric tensor
Symmetric (0,2) tensor g_{μν} that defines distances, angles, and proper times on a manifold. ds² = g_{μν} dx^μ dx^ν. In flat SR spacetime g = η = diag(+1, −1, −1, −1); in GR g_{μν}(x) varies with position and encodes all gravitational information.
Mode
An allowed standing-wave pattern of a bounded system, labelled by an integer.
Moment arm
The perpendicular distance from a rotation axis to the line of action of a force. Torque = force × moment arm.
moment of inertia
The rotational analogue of mass: I = Σ m_i · r_i² (or ∫ r² dm for a continuous body).
momentum
Mass times velocity (a vector, p = m·v); conserved in any closed system.
Motional EMF
The EMF induced in a conductor moving through a magnetic field, driven by the magnetic part of the Lorentz force on free charges inside the conductor. Equals (v × B) · ℓ for a straight rod of length ℓ moving with velocity v in field B.
Mutual inductance
The coupling between two separated coils: M = Φ₁₂/I₂, the flux that coil 2's current produces through coil 1 per unit coil-2 current. The operating principle of every transformer.
Navier-Stokes equations
The PDEs governing viscous fluid flow. Nonlinear, exact, and generally unsolved — smoothness in 3D is a Millennium Problem.
Near-field zone
The region r ≪ λ surrounding an oscillating source where the field resembles a time-varying instantaneous quasi-static field (amplitude ∝ 1/r³ for a dipole) that stores and returns energy rather than radiating it. Also called the induction zone or reactive zone.
Newton's laws of motion
The three laws — inertia, F = ma, and equal-and-opposite reaction — that launched classical mechanics in 1687.
Newtonian fluid
A fluid whose shear stress is strictly proportional to its velocity gradient, with viscosity independent of shear rate.
Newtonian limit
The regime where Einstein's field equations reduce to Newton's: weak gravity (g_{μν} = η_{μν} + h_{μν}, |h| ≪ 1), slow sources (v ≪ c), static configuration. In this limit G_{00} ≈ −2∇²Φ/c² and T_{00} ≈ ρc², so EFE becomes ∇²Φ = 4πGρ — the Poisson equation of Newtonian gravity.
Node
A point on a standing wave that never moves.
Noether's theorem
Every continuous symmetry of a physical system's action gives rise to a conserved quantity.
Non-abelian gauge theory
A gauge theory whose gauge group is non-commutative, so the gauge fields themselves carry charge under the group and the field strength tensor acquires a self-interaction term. Yang-Mills 1954 introduced the construction; QCD and the weak force are non-abelian; QED is the abelian exception.
nonlinear dynamics
Study of systems where output is not proportional to input; chaos, solitons, turbulence.