This article summarizes equations in the theory of electromagnetism.
Definitions
Here subscripts e and m are used to differ between electric and magnetic charges. The definitions for monopoles are of theoretical interest, although real magnetic dipoles can be described using pole strengths. There are two possible units for monopole strength, Wb (Weber) and A m (Ampere metre). Dimensional analysis shows that magnetic charges relate by qm(Wb) = μ0 qm(Am).
Initial quantities
Quantity (common name/s) (Common) symbol/s SI units DimensionElectric charge qe, q, Q C = As [I][T] Monopole strength, magnetic charge qm, g, p Wb or Am [L]2[M][T]−2 [I]−1 (Wb) [I][L] (Am)
Electric quantities
Contrary to the strong analogy between (classical) gravitation and electrostatics, there are no "centre of charge" or "centre of electrostatic attraction" analogues.
Electric transport
Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Linear, surface, volumetric charge density λe for Linear, σe for surface, ρe for volume. C m−n, n = 1, 2, 3 [I][T][L]−nCapacitance CV = voltage, not volume. F = C V−1 [I]2[T]4[L]−2[M]−1 Electric current I A [I]Electric current density J A m−2 [I][L]−2Displacement current density Jd A m−2 [I][L]−2Convection current density Jc A m−2 [I][L]−2
Electric fields
Quantity (common name/s) (Common) symbol/s Defining equation SI units DimensionElectric field, field strength, flux density, potential gradient E N C−1 = V m−1 [M][L][T]−3[I]−1Electric flux ΦE N m2 C−1 [M][L]3[T]−3[I]−1Absolute permittivity; ε F m−1 [I]2 [T]4 [M]−1 [L]−3 Electric dipole moment pa = charge separation directed from -ve to +ve charge C m [I][T][L]Electric Polarization, polarization density P C m−2 [I][T][L]−2Electric displacement field, flux density D C m−2 [I][T][L]−2Electric displacement flux ΦD C [I][T]Absolute electric potential, EM scalar potential relative to point
Theoretical: Practical: (Earth's radius) φ ,V V = J C−1 [M] [L]2 [T]−3 [I]−1Voltage, Electric potential difference Δφ,ΔV V = J C−1 [M] [L]2 [T]−3 [I]−1
Magnetic quantities
Magnetic transport
Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Linear, surface, volumetric pole density λm for Linear, σm for surface, ρm for volume. Wb m−n A m(−n + 1), n = 1, 2, 3 [L]2[M][T]−2 [I]−1 (Wb) [I][L] (Am)Monopole current Im Wb s−1 A m s−1[L]2[M][T]−3 [I]−1 (Wb) [I][L][T]−1 (Am)Monopole current density Jm Wb s−1 m−2 A m−1 s−1[M][T]−3 [I]−1 (Wb) [I][L]−1[T]−1 (Am)
Magnetic fields
Quantity (common name/s) (Common) symbol/s Defining equation SI units DimensionMagnetic field, field strength, flux density, induction field B T = N A−1 m−1 = Wb m−2 [M][T]−2[I]−1 Magnetic potential, EM vector potential A T m = N A−1 = Wb m3 [M][L][T]−2[I]−1 Magnetic flux ΦB Wb = T m2 [L]2[M][T]−2[I]−1Magnetic permeability V·s·A−1·m−1 = N·A−2 = T·m·A−1 = Wb·A−1·m−1 [M][L][T]−2[I]−2 Magnetic moment, magnetic dipole moment m, μB, ΠTwo definitions are possible:
using pole strengths,
using currents:
a = pole separation
N is the number of turns of conductor A m2 [I][L]2Magnetization M A m−1 [I] [L]−1Magnetic field intensity, (AKA field strength) H Two definitions are possible:
most common:
using pole strengths, A m−1 [I] [L]−1Intensity of magnetization, magnetic polarization I, J T = N A−1 m−1 = Wb m−2 [M][T]−2[I]−1 Self Inductance L Two equivalent definitions are possible: H = Wb A−1 [L]2 [M] [T]−2 [I]−2 Mutual inductance M Again two equivalent definitions are possible:
1,2 subscripts refer to two conductors/inductors mutually inducing voltage/ linking magnetic flux through each other. They can be interchanged for the required conductor/inductor;
H = Wb A−1 [L]2 [M] [T]−2 [I]−2Gyromagnetic ratio (for charged particles in a magnetic field) γ Hz T−1 [M]−1[T][I]
Electric circuits
DC circuits, general definitions
Quantity (common name/s) (Common) symbol/s Defining equation SI units DimensionTerminal Voltage for power supply Vter V = J C−1 [M] [L]2 [T]−3 [I]−1Load Voltage for CircuitVload V = J C−1 [M] [L]2 [T]−3 [I]−1Internal resistance of power supply Rint Ω = V A−1 = J s C−2 [M][L]2 [T]−3 [I]−2Load resistance of circuit Rext Ω = V A−1 = J s C−2 [M][L]2 [T]−3 [I]−2Electromotive force (emf), voltage across entire circuit including power supply, external components and conductors E V = J C−1 [M] [L]2 [T]−3 [I]−1
AC circuits
Quantity (common name/s) (Common) symbol/s Defining equation SI units DimensionResistive load voltage VR V = J C−1 [M] [L]2 [T]−3 [I]−1Capacitive load voltage VC V = J C−1 [M] [L]2 [T]−3 [I]−1Inductive load voltageVL V = J C−1 [M] [L]2 [T]−3 [I]−1Capacitive reactanceXC Ω−1 m−1 [I]2 [T]3 [M]−2 [L]−2 Inductive reactanceXL Ω−1 m−1 [I]2 [T]3 [M]−2 [L]−2 AC electrical impedance Z Ω−1 m−1 [I]2 [T]3 [M]−2 [L]−2 Phase constant δ, φdimensionlessdimensionlessAC peak current I0 A [I]AC root mean square currentIrms A [I]AC peak voltageV0 V = J C−1 [M] [L]2 [T]−3 [I]−1AC root mean square voltageVrms V = J C−1 [M] [L]2 [T]−3 [I]−1AC emf, root mean square V = J C−1 [M] [L]2 [T]−3 [I]−1AC average power W = J s−1 [M] [L]2 [T]−3Capacitive time constant τC s [T]Inductive time constant τL s [T]
Magnetic circuits
Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Magnetomotive force, mmf F,
N = number of turns of conductor A [I]
Electromagnetism
Electric fields
General Classical Equations
Physical situation EquationsElectric potential gradient and field Point charge At a point in a local array of point charges At a point due to a continuum of charge Electrostatic torque and potential energy due to non-uniform fields and dipole moments
Magnetic fields and moments
General classical equations
Physical situation EquationsMagnetic potential, EM vector potential Due to a magnetic moment Magnetic moment due to a current distribution Magnetostatic torque and potential energy due to non-uniform fields and dipole moments
Electric circuits and electronics
Below N = number of conductors or circuit components. Subscript net refers to the equivalent and resultant property value.
Physical situation Nomenclature Series ParallelResistors and conductorsRi = resistance of resistor or conductor i Gi = conductance of resistor or conductor i Charge, capacitors, currents Ci = capacitance of capacitor i qi = charge of charge carrier i Inductors Li = self-inductance of inductor i Lij = self-inductance element ij of L matrix Mij = mutual inductance between inductors i and j Circuit DC Circuit equations AC Circuit equations+Series circuit equationsRC circuitsCircuit equation
Capacitor charge
Capacitor dischargeRL circuitsCircuit equation
Inductor current rise
Inductor current fallLC circuitsCircuit equationCircuit equation
Circuit resonant frequency
Circuit charge
Circuit current
Circuit electrical potential energy
Circuit magnetic potential energyRLC circuitsCircuit equationCircuit equation
Circuit charge
See also Defining equation (physical chemistry) Fresnel equations Maxwell's equations List of equations in classical mechanics List of equations in fluid mechanics List of equations in gravitation List of equations in nuclear and particle physics List of equations in quantum mechanics List of equations in wave theory List of photonics equations List of relativistic equations SI electromagnetism units Table of thermodynamic equations
Footnotes
Sources
Further reading