Electromagnetism unifies electricity, magnetism, optics, and radiation, forming the physical bedrock of electrical engineering, wireless communications, semiconductor devices, and astrophysics. From Coulomb's inverse-square electrostatic force to Maxwell's symmetric field equations, electromagnetic interactions govern physical phenomena across both macroscopic and microscopic scales through rigorous mathematical laws.
This cheat sheet systematically organizes 20 core physical laws and foundational equations in electromagnetism, partitioned into Electrostatics & Fields, Circuits & Magnetostatics, Electromagnetic Induction, and Maxwell's Equations, clearly presenting standard mathematical expressions, key variable definitions, physical principles, validity domains, and engineering applications.
🔗 Physics Laws & Equations Matrix: Classical Mechanics & Motion · Fluid Dynamics & Thermodynamics · Optics & Acoustics · Nuclear & Particle Physics · Relativity & Cosmology · Astrophysics & Geophysics · Quantum Mechanics
1. Electrostatics & Fields (5 Laws)
Electrostatics describes the fields generated by charges at relative rest, establishing Coulomb interactions, electric field intensity, scalar potential, and electrostatic Gauss flux conservation.
01 · Coulomb's Law
Coulomb's Law
$$F = k \frac{q_1 q_2}{r^2} = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r^2}$$
- ①Physical Essence: The electrostatic force between two stationary point charges in vacuum is directly proportional to the product of their charges and inversely proportional to the square of their separation distance. Like charges repel; opposite charges attract.
- ②Variable Definitions: $k = 1/(4\pi\varepsilon_0) \approx 8.98755 \times 10^9\;\text{N}\cdot\text{m}^2/\text{C}^2$ is Coulomb's electrostatic constant, $\varepsilon_0$ is the vacuum permittivity, $q_1, q_2$ are charge magnitudes ($\text{C}$), and $r$ is separation distance ($\text{m}$).
- ③Fundamental Significance: The experimental foundation of electrostatics, structurally identical to Newton's universal gravitation, governing atomic electron shells and chemical bonding.
- ④Validity Domain & Applications: Strictly valid for stationary point charges in vacuum; moving charges generate magnetic fields and retarded potentials. Applied in electrostatic spray painting, industrial precipitators, ESD mitigation, and Rutherford atomic models.
02 · Electric Field
Electric Field Intensity
$$\mathbf{E} = \frac{\mathbf{F}}{q_0} \quad \left(\mathbf{E} = \frac{1}{4\pi\varepsilon_0}\frac{Q}{r^2}\hat{\mathbf{r}}\right)$$
- ①Physical Essence: The electrostatic force per unit positive test charge exerted at a point in space; field is the physical mediator of electric force, replacing the historical concept of "action-at-a-distance".
- ②Variable Definitions: $\mathbf{E}$ is electric field vector ($\text{N/C}$ or $\text{V/m}$), $\mathbf{F}$ is electrostatic force, and $q_0$ is an infinitesimal positive test charge (small enough not to perturb source charge distributions).
- ③Fundamental Significance: The core vector quantity characterizing electrostatic and induced vortex electric fields; field line tangents give direction, line density represents field magnitude.
- ④Validity Domain & Applications: Valid for both static and time-varying fields. Applied in cathode ray oscilloscope deflection plates, high-voltage insulation design, and dielectric breakdown evaluation (dielectric strength of dry air $\sim 3\;\text{kV/mm}$).
03 · Gauss's Law for Electrostatics
Gauss's Flux Theorem
$$\oint_{S} \mathbf{E}\cdot\mathrm{d}\mathbf{A} = \frac{Q_{\text{enc}}}{\varepsilon_0} \iff \nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}$$
- ①Physical Essence: The net electric flux through any closed Gaussian surface is proportional to the total enclosed charge. Demonstrates that electrostatic fields are divergence sources: positive charges act as sources, negative charges as sinks.
- ②Variable Definitions: $\mathbf{E}$ is electric field vector, $\mathrm{d}\mathbf{A}$ is outward normal area element, $Q_{\text{enc}}$ is total enclosed charge, and $\rho$ is free volume charge density.
- ③Fundamental Significance: The first of Maxwell's equations, providing the rigorous integral form of Coulomb's inverse-square geometry.
- ④Validity Domain & Applications: Universally valid for any closed surface. Enables rapid calculation of field distributions in spherically, cylindrically, or planar-symmetric charge geometries; guides Faraday cage shielding and coaxial cable electromagnetic screening.
04 · Electric Potential Difference
Electric Potential & Voltage
$$V = \frac{W_{AB}}{q} \iff \Delta V = -\int_{A}^{B} \mathbf{E}\cdot\mathrm{d}\mathbf{r}$$
- ①Physical Essence: The electrostatic field is a conservative force field (curl-free); the work done by electric forces in moving a unit positive charge from point A to B depends solely on end-points, independent of traversed path.
- ②Variable Definitions: $V$ is electric potential difference/voltage ($\text{V}$), $W_{AB}$ is electrostatic work performed ($\text{J}$), $q$ is test charge, and $\mathbf{E} = -\nabla V$ connects electric field to negative potential gradient.
- ③Fundamental Significance: Theoretical foundation of circuit analysis and macroscopic voltage definition; arbitrary reference ground potential selection leaves physical potential differences invariant.
- ④Validity Domain & Applications: Strictly valid for irrotational electrostatic fields and stationary currents without magnetic induction. Applied in particle accelerator voltages, electrochemical EMF metrology, and IC power distribution networks.
05 · Electric Dipole Moment
Electric Dipole Moment
$$\mathbf{p} = q\mathbf{d} \quad (\boldsymbol{\tau} = \mathbf{p}\times\mathbf{E})$$
- ①Physical Essence: Quantifies the degree of spatial charge separation in a system of equal and opposite charges; the dipole vector points strictly from negative toward positive charge.
- ②Variable Definitions: $\mathbf{p}$ is electric dipole moment ($\text{C}\cdot\text{m}$), $q$ is charge magnitude, $\mathbf{d}$ is displacement vector from negative to positive pole, and $\boldsymbol{\tau}$ is restoring torque experienced in an external electric field.
- ③Fundamental Significance: Paramount parameter in molecular polarity characterization, dielectric polarization modeling, and dipole antenna electromagnetic radiation.
- ④Validity Domain & Applications: Dipole far-field approximation ($r \gg d$). Applied in water molecule dielectric polarity explanations, microwave oven dielectric heating resonance, material permittivity testing, and RF dipole antennas.
2. Circuits & Magnetostatics (7 Laws)
Steady currents propagate through conductors governed by Ohm's transport and Joule dissipation, generating magnetostatic fields that exert Ampère and Lorentz forces on moving charges and currents.
06 · Ohm's Law
Ohm's Law
$$V = IR \iff \mathbf{J} = \sigma \mathbf{E}$$
- ①Physical Essence: Current flowing through a linear conductor is directly proportional to applied voltage and inversely proportional to electrical resistance. The microscopic differential formulation states that current density is proportional to local electric field.
- ②Variable Definitions: $V$ is potential difference ($\text{V}$), $I$ is current ($\text{A}$), $R$ is resistance ($\Omega$), $\mathbf{J}$ is current density ($\text{A/m}^2$), and $\sigma$ is electrical conductivity ($\text{S/m}$).
- ③Fundamental Significance: The analytical foundation of electrical engineering and Kirchhoff's laws, providing the starting point for all linear lumped-parameter network calculations.
- ④Validity Domain & Applications: Valid for linear Ohmic conductors (metals, electrolytes); non-linear devices (diodes, transistors, gas discharge tubes) do not follow Ohm's law. Applied in power distribution, signal resistor dividing, and sensor calibration.
07 · Resistance of a Conductor
Conductor Resistance Formula
$$R = \rho \frac{L}{A}$$
- ①Physical Essence: Resistance of a uniform cross-section conductor is proportional to its material resistivity and length, and inversely proportional to its cross-sectional area.
- ②Variable Definitions: $R$ is resistance ($\Omega$), $\rho$ is material resistivity ($\Omega\cdot\text{m}$), $L$ is conductor length ($\text{m}$), and $A$ is conducting cross-sectional area ($\text{m}^2$).
- ③Fundamental Significance: Guides electrical cable sizing, PCB copper trace width optimization, and resistive transducer sensing.
- ④Validity Domain & Applications: Resistivity varies with temperature (metals increase with temperature; semiconductors decrease). Applied in PCB trace impedance sizing, strain gauges, potentiometers, and heating element alloy selection.
08 · Joule's Law
Joule Heating
$$Q = I^2 R t \quad (P = I^2 R = UI)$$
- ①Physical Essence: Heat generated by an electric current passing through a conductor is proportional to the square of current intensity, resistance, and conduction duration. Represents irreversible ohmic dissipation into internal thermal energy.
- ②Variable Definitions: $Q$ is dissipated Joule heat ($\text{J}$), $I$ is current ($\text{A}$), $R$ is resistance ($\Omega$), $t$ is duration ($\text{s}$), and $P$ is thermal dissipation power ($\text{W}$).
- ③Fundamental Significance: Essential physical law for electric heater engineering, power grid transmission loss budgeting, and power semiconductor thermal management.
- ④Validity Domain & Applications: Strictly holds for resistive dissipation; in non-purely resistive loads (motors, batteries), total electrical energy input $W = UIt > I^2 Rt$. High-voltage transmission drastically reduces $I^2 R$ transmission line losses by lowering current.
09 · Biot-Savart Law
Biot-Savart Law
$$\mathrm{d}\mathbf{B} = \frac{\mu_0}{4\pi}\frac{I\mathrm{d}\mathbf{l}\times\hat{\mathbf{r}}}{r^2}$$
- ①Physical Essence: Governs the infinitesimal magnetic field element generated at a point in space by a steady current element; direction follows the right-hand cross product rule. Analogous to Coulomb's differential superposition in magnetostatics.
- ②Variable Definitions: $\mathrm{d}\mathbf{B}$ is magnetic flux density element ($\text{T}$), $\mu_0 = 4\pi \times 10^{-7}\;\text{T}\cdot\text{m/A}$ is vacuum permeability, $I$ is current, $\mathrm{d}\mathbf{l}$ is directed current path element, and $r$ is displacement distance to field point.
- ③Fundamental Significance: The fundamental differential integral tool for computing magnetostatic fields generated by arbitrary current-carrying geometries.
- ④Validity Domain & Applications: Strictly valid for steady, closed electrical current loops. Applied in calculating magnetic fields of long straight wires, circular coils, Helmholtz coils, and solenoids.
10 · Ampère's Circuital Law
Ampère's Circuital Law (Static Magnetism)
$$\oint_{C} \mathbf{B}\cdot\mathrm{d}\mathbf{l} = \mu_0 I_{\text{enc}} \iff \nabla \times \mathbf{B} = \mu_0 \mathbf{J}$$
- ①Physical Essence: The line integral of steady magnetic flux density along any closed loop is proportional to the total net conduction current threading through the loop. Demonstrates that steady magnetic fields are solenoidal and rotational.
- ②Variable Definitions: $\mathbf{B}$ is magnetic field vector, $\mathrm{d}\mathbf{l}$ is loop displacement element, $\mu_0$ is permeability, $I_{\text{enc}}$ is enclosed current, and $\mathbf{J}$ is conduction current density.
- ③Fundamental Significance: The most efficient analytical method for evaluating highly symmetric magnetic fields, subsequently extended by Maxwell with the displacement current term.
- ④Validity Domain & Applications: Strictly valid for steady DC currents; non-steady time-dependent fields with capacitors require displacement currents. Applied in coaxial cables, toroidal inductors, and magnetic core transformer circuits.
11 · Lorentz Force
Lorentz Force Law
$$\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$$
- ①Physical Essence: The net electromagnetic force experienced by a moving charged particle in combined electric and magnetic fields, comprising electric component $q\mathbf{E}$ and magnetic component $q(\mathbf{v}\times\mathbf{B})$.
- ②Variable Definitions: $q$ is particle charge, $\mathbf{E}$ is electric field, $\mathbf{v}$ is velocity vector, $\mathbf{B}$ is magnetic field, and $\times$ denotes vector cross product.
- ③Fundamental Significance: The dynamic bridge linking electromagnetic fields to particle trajectory kinematics; **magnetic forces act perpendicular to velocity and therefore do no mechanical work (altering trajectory direction without modifying kinetic energy)**.
- ④Validity Domain & Applications: Valid across classical and relativistic particle dynamics. Applied in cathode ray tubes (CRT), cyclotrons, mass spectrometers, and Tokamak magnetic confinement fusion devices.
12 · Ampère Force
Magnetic Force on Current-Carrying Wire
$$F = B I L \sin\theta \iff \mathrm{d}\mathbf{F} = I\mathrm{d}\mathbf{l}\times\mathbf{B}$$
- ①Physical Essence: Force exerted by an external magnetic field on a current-carrying conductor; direction is given by Fleming's left-hand rule.
- ②Variable Definitions: $F$ is magnetic force ($\text{N}$), $B$ is flux density ($\text{T}$), $I$ is current ($\text{A}$), $L$ is wire length ($\text{m}$), and $\theta$ is angle between current and magnetic field vectors.
- ③Fundamental Significance: The driving mechanism behind electric motors, galvanometers, and electromagnetic propulsion, representing the macroscopic summation of microscopic Lorentz forces acting on mobile charge carriers.
- ④Validity Domain & Applications: Force is zero when current is parallel to field ($\sin\theta = 0$), maximum when perpendicular. Applied in AC/DC electric motors, voice-coil speakers, maglev vehicle propulsion, and railgun acceleration systems.
3. Electromagnetic Induction (4 Laws)
Time-varying magnetic flux induces electric fields, creating the physical foundation of modern power generation, transmission networks, and electromechanical machinery.
13 · Faraday's Law of Induction
Faraday's Law of Induction
$$\mathcal{E} = -\frac{\mathrm{d}\Phi}{\mathrm{d}t} \iff \oint_{C} \mathbf{E}\cdot\mathrm{d}\mathbf{l} = -\frac{\mathrm{d}}{\mathrm{d}t}\iint_{S}\mathbf{B}\cdot\mathrm{d}\mathbf{A}$$
- ①Physical Essence: When magnetic flux threading a circuit changes, an electromotive force (EMF) is induced proportional to the time rate of change of magnetic flux; the negative sign reflects Lenz's law.
- ②Variable Definitions: $\mathcal{E}$ is induced EMF ($\text{V}$), $\Phi$ is magnetic flux ($\text{Wb}$), and $t$ is time. For an $N$-turn coil, induced EMF is $-N\,\mathrm{d}\Phi/\mathrm{d}t$.
- ③Fundamental Significance: The third Maxwell equation, establishing that changing magnetic fields produce circulating vortex electric fields in empty space.
- ④Validity Domain & Applications: Encompasses both motional EMF (Lorentz force on moving conductors) and transformer EMF (induced electric field). Applied in power generators, grid transformers, induction motors, and eddy current induction cooktops.
14 · Lenz's Law
Lenz's Law (Direction of Induced Currents)
$$\Delta\Phi_{\text{ind}} \propto -\Delta\Phi_{\text{ext}}$$
- ①Physical Essence: **The direction of an induced current in a closed loop always generates a secondary magnetic flux that opposes the change in primary magnetic flux that created it**. Manifestation of energy conservation in electromagnetic systems.
- ②Variable Definitions: $\Delta\Phi_{\text{ext}}$ is external magnetic flux variation, and $\Delta\Phi_{\text{ind}}$ is induced counter-flux. If external flux increases, induced field opposes it; if flux decreases, induced field reinforces it.
- ③Fundamental Significance: The universal rule for determining the polarity and direction of induced EMFs, directly accounting for the negative sign in Faraday's formulation.
- ④Validity Domain & Applications: Closed loops generate counter-currents; open circuits generate opposing EMFs. Applied in electromagnetic regenerative braking, eddy current vibration dampers, ballistic galvanometers, and metal detectors.
15 · Self-Induced EMF
Self-Inductance & Back EMF
$$\mathcal{E} = -L\frac{\mathrm{d}I}{\mathrm{d}t} \quad \left(W_m = \frac{1}{2}LI^2\right)$$
- ①Physical Essence: An electromotive force induced in an electrical circuit due to time variations of the current flowing through that circuit itself; inductance measures circuit "electrical inertia" opposing current fluctuations.
- ②Variable Definitions: $\mathcal{E}$ is self-induced EMF ($\text{V}$), $L$ is self-inductance ($\text{H}$), $I$ is current, $t$ is time, and $W_m$ is magnetic energy stored in the inductor ($\text{J}$).
- ③Fundamental Significance: Defining governing law for inductive circuit elements, dictating that current through an inductor cannot change instantaneously.
- ④Validity Domain & Applications: Interrupted high-inductance circuits experience large $\mathrm{d}I/\mathrm{d}t$, generating kilovolt transient voltage spikes and inductive arcing. Applied in switch-mode power supply filter chokes, LC oscillators, and relay flyback diode protection.
16 · Magnetic Flux
Magnetic Flux
$$\Phi = B A \cos\theta = \iint_{S} \mathbf{B}\cdot\mathrm{d}\mathbf{A}$$
- ①Physical Essence: The total surface integral of magnetic flux density passing through a given surface area; core state variable quantifying spatial magnetic field distributions.
- ②Variable Definitions: $\Phi$ is magnetic flux in Webers ($\text{Wb} = \text{T}\cdot\text{m}^2 = \text{V}\cdot\text{s}$), $B$ is flux density, $A$ is area, and $\theta$ is angle between magnetic field and surface normal.
- ③Fundamental Significance: Primary input variable for induction; according to Gauss's law for magnetism, net magnetic flux through any closed surface is identically zero ($\oint \mathbf{B}\cdot\mathrm{d}\mathbf{A} = 0$).
- ④Validity Domain & Applications: Magnetic flux quantization in superconductors ($\Phi_0 = h/(2e) \approx 2.07 \times 10^{-15}\;\text{Wb}$) underpins Superconducting Quantum Interference Devices (SQUIDs). Applied in transformer core cross-section sizing, fluxgate magnetometers, and magnetic shielding.
4. Maxwell's Equations (4 Laws)
Maxwell's equations unify electricity, magnetism, and optics into a symmetric set of partial differential equations, predicting electromagnetic waves and crowning classical field theory.
17 · Maxwell: Gauss & Ampère-Maxwell
Maxwell Equations (1 & 2)
$$\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}, \quad \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0\varepsilon_0\frac{\partial \mathbf{E}}{\partial t}$$
- ①Physical Essence: The first equation establishes that electric charges are divergence sources of electric fields; the second establishes that magnetic curl fields are generated by both conduction currents and **time-varying electric fields (displacement current)**.
- ②Variable Definitions: $\mathbf{E}$ is electric field, $\mathbf{B}$ is magnetic field, $\rho$ is charge density, $\mathbf{J}$ is conduction current density, and $\mathbf{J}_D = \varepsilon_0(\partial\mathbf{E}/\partial t)$ is displacement current density.
- ③Fundamental Significance: Maxwell's displacement current hypothesis restored charge conservation consistency in non-steady circuits, forming a symmetric dynamic loop between electricity and magnetism.
- ④Validity Domain & Applications: Foundational canon of classical electrodynamics. Explains the origin of magnetic fields between capacitor plates during charging/discharging, serving as the basis of antenna radiation theory.
18 · Maxwell: Gauss for B & Faraday
Maxwell Equations (3 & 4)
$$\nabla \cdot \mathbf{B} = 0, \quad \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$$
- ①Physical Essence: The third equation states that magnetic fields have zero divergence (no isolated magnetic monopoles exist; magnetic field lines are always closed loops); the fourth states that time-varying magnetic fields curl to produce vortex electric fields.
- ②Variable Definitions: $\nabla\cdot$ is divergence operator, $\nabla\times$ is curl operator, and $\partial\mathbf{B}/\partial t$ is time rate of change of magnetic field.
- ③Fundamental Significance: Paired with displacement current, these dual equations yield electromagnetic wave equations in source-free vacuum, formally unifying electricity, magnetism, and light.
- ④Validity Domain & Applications: If experimental magnetic monopoles are discovered, dual source terms will be added. Applied in electromagnetic wave propagation, waveguide modal analysis, and radar antenna radiation simulations.
19 · Speed of Electromagnetic Waves
Wave Velocity & Speed of Light
$$c = \frac{1}{\sqrt{\varepsilon_0 \mu_0}} \approx 3.00\times 10^8\text{ m/s}$$
- ①Physical Essence: The phase velocity of electromagnetic waves in vacuum is exclusively determined by two electrostatic and magnetostatic constants: $\varepsilon_0$ and $\mu_0$; **first theoretical proof that light is an electromagnetic wave**.
- ②Variable Definitions: $c$ is electromagnetic wave speed in vacuum ($299,792,458\;\text{m/s}$ exact), $\varepsilon_0$ is permittivity, and $\mu_0$ is permeability. In a dielectric medium, phase velocity is $v = 1/\sqrt{\varepsilon\mu} = c/n$.
- ③Fundamental Significance: One of the greatest unifications in scientific history, directly inspiring Einstein's principle of the constancy of the speed of light in special relativity.
- ④Validity Domain & Applications: Universal causal speed limit in vacuum. Applied in fiber optic latency modeling, deep-space telemetry, and GNSS satellite ranging triangulation ($d = c \cdot \Delta t$).
20 · Poynting Vector
Electromagnetic Energy Flux
$$\mathbf{S} = \mathbf{E} \times \mathbf{H} = \frac{1}{\mu_0}(\mathbf{E}\times\mathbf{B})$$
- ①Physical Essence: Directional energy flux density of an electromagnetic field; vector magnitude represents energy transmitted per unit time per unit area normal to propagation direction.
- ②Variable Definitions: $\mathbf{S}$ is Poynting vector ($\text{W/m}^2$), $\mathbf{E}$ is electric field, $\mathbf{H} = \mathbf{B}/\mu$ is magnetic field intensity, and $\mathbf{B}$ is magnetic flux density.
- ③Fundamental Significance: Core flux term in Poynting's theorem of electromagnetic energy conservation, proving that electromagnetic fields carry both energy and linear momentum.
- ④Validity Domain & Applications: Valid in wave radiation zones and near guided wave transmission lines. Applied in base station RF power density compliance, solar radiation pressure calculations ($P_{\text{rad}} = S/c$), and laser sail propulsion design.
5. Physical Quantities, Symbols, and SI Units
| Physical Quantity | Symbol | Scalar / Vector | SI Base or Derived Unit | SI Symbol | Equivalence & Conversions |
|---|---|---|---|---|---|
| Electric Charge | $Q, q$ | Scalar | Coulomb | C | $1;\text{C} = 1;\text{A}\cdot\text{s}$ |
| Electric Current | $I, i$ | Scalar (circuit) / Vector (density) | Ampere (SI Base Unit) | A | $1;\text{A} = 1;\text{C/s}$ |
| Current Density | $\mathbf{J}$ | Vector | Amperes per square meter | $\text{A/m}^2$ | $J = I/A$ |
| Electric Field | $\mathbf{E}$ | Vector | Volts per meter / Newtons per Coulomb | V/m, N/C | $1;\text{V/m} = 1;\text{N/C}$ |
| Electric Potential / Voltage | $V, U, \varphi$ | Scalar | Volt | V | $1;\text{V} = 1;\text{J/C} = 1;\text{W/A}$ |
| Capacitance | $C$ | Scalar | Farad | F | $1;\text{F} = 1;\text{C/V}$ |
| Electric Displacement | $\mathbf{D}$ | Vector | Coulombs per square meter | $\text{C/m}^2$ | $\mathbf{D} = \varepsilon_0 \mathbf{E} + \mathbf{P}$ |
| Permittivity | $\varepsilon$ | Scalar / Tensor | Farads per meter | F/m | $\varepsilon_0 \approx 8.854 \times 10^{-12};\text{F/m}$ |
| Resistance | $R$ | Scalar | Ohm | $\Omega$ | $1;\Omega = 1;\text{V/A}$ |
| Resistivity | $\rho$ | Scalar | Ohm-meter | $\Omega\cdot\text{m}$ | $\rho = R A / L$ |
| Conductivity | $\sigma$ | Scalar | Siemens per meter | S/m | $\sigma = 1/\rho$ |
| Magnetic Flux Density | $\mathbf{B}$ | Vector | Tesla | T | $1;\text{T} = 1;\text{N/(A}\cdot\text{m)} = 1;\text{Wb/m}^2 = 10^4;\text{Gs}$ |
| Magnetic Field Intensity | $\mathbf{H}$ | Vector | Amperes per meter | A/m | $\mathbf{B} = \mu_0(\mathbf{H} + \mathbf{M})$ |
| Magnetic Flux | $\Phi$ | Scalar | Weber | Wb | $1;\text{Wb} = 1;\text{T}\cdot\text{m}^2 = 1;\text{V}\cdot\text{s}$ |
| Inductance (Self/Mutual) | $L, M$ | Scalar | Henry | H | $1;\text{H} = 1;\text{Wb/A} = 1;\text{V}\cdot\text{s/A}$ |
| Permeability | $\mu$ | Scalar / Tensor | Henrys per meter | H/m | $\mu_0 = 4\pi \times 10^{-7};\text{H/m} \approx 1.257 \times 10^{-6};\text{H/m}$ |
| Electric Dipole Moment | $\mathbf{p}$ | Vector | Coulomb-meter | $\text{C}\cdot\text{m}$ | $\mathbf{p} = q\mathbf{d}$ |
| Poynting Energy Flux | $\mathbf{S}$ | Vector | Watts per square meter | $\text{W/m}^2$ | $1;\text{W/m}^2 = 1;\text{J/(s}\cdot\text{m}^2)$ |