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 q_{m}(Wb) = μ_{0} q_{m}(Am).
Initial quantities

Quantity (common name/s) (Common) symbol/s SI units Dimension Electric charge q_{e}, q, Q C = As [I][T] Monopole strength, magnetic charge q_{m}, 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 λ_{e} for Linear, σ_{e} for surface, ρ_{e} for volume. C m^{−n}, n = 1, 2, 3 [I][T][L]^{−n} Capacitance C V = voltage, not volume.
F = C V^{−1} [I][T]^{3}[L]^{−2}[M]^{−1} Electric current I A [I] Electric current density J A m^{−2} [I][L]^{−2} Displacement current density J_{d} Am^{−2} [I][L]m^{−2} Convection current density J_{c} A m^{−2} [I] [L]m^{−2}
Electric fields

Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Electric field, field strength, flux density, potential gradient E N C^{−1} = V m^{−1} [M][L][T]^{−3}[I]^{−1} Electric flux Φ_{E} N m^{2} C^{−1} [M][L]^{3}[T]^{−3}[I]^{−1} Absolute permittivity; ε F m^{−1} [I]^{2} [T]^{4} [M]^{−1} [L]^{−3} Electric dipole moment p a = charge separation directed from ve to +ve charge
C m [I][T][L] Electric Polarization, polarization density P C m^{−2} [I][T][L]^{−2} Electric displacement field D C m^{−2} [I][T][L]^{−2} Electric displacement flux Φ_{D} C [I][T] Absolute electric potential, EM scalar potential relative to point Theoretical:
Practical:φ ,V V = J C^{−1} [M] [L]^{2} [T]^{−3} [I]^{−1} Voltage, 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 λ_{m} for Linear, σ_{m} for surface, ρ_{m} 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 I_{m} Wb s^{−1} A m s^{−1}
[L]^{2}[M][T]^{−3} [I]^{−1} (Wb) [I][L][T]^{−1} (Am)
Monopole current density J_{m} 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 Dimension Magnetic 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 m^{3} [M][L][T]^{−2}[I]^{−1} Magnetic flux Φ_{B} Wb = T m^{−2} [L]^{2}[M][T]^{−2}[I]^{−1} Magnetic 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, μ_{B}, Π Two definitions are possible:
using pole strengths,
using currents:
a = pole separation N is the number of turns of conductor
A m^{2} [I][L]^{2} Magnetization M A m^{2} [I] [L]^{−1} Magnetic field intensity, (AKA field strength) H Two definitions are possible: most common:
using pole strengths,^{[1]}
A m^{−1} [I] [L]^{−1} Intensity 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 though each other. They can be interchanged for the required conductor/inductor;
H = Wb A^{−1} [L]^{2} [M] [T]^{−2} [I]^{−2} Gyromagnetic ratio (for charged particles in a magnetic field) γ Hz T^{−1} [M]^{−1}[T][I]
Electric circuits
DC circuits, general definitions
Main article: Direct current

Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Terminal Voltage for V_{ter} V = J C^{−1} [M] [L]^{2} [T]^{−3} [I]^{−1} Load Voltage for Circuit V_{load} V = J C^{−1} [M] [L]^{2} [T]^{−3} [I]^{−1} Internal resistance of power supply R_{int} Ω = V A^{−1} = J s C^{−2} [M][L]^{2} [T]^{−3} [I]^{−2} Load resistance of circuit R_{ext} Ω = V A^{−1} = J s C^{−2} [M][L]^{2} [T]^{−3} [I]^{−2} Electromotive 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 Dimension Resistive load voltage V_{R} V = J C^{−1} [M] [L]^{2} [T]^{−3} [I]^{−1} Capacitive load coltage V_{C} V = J C^{−1} [M] [L]^{2} [T]^{−3} [I]^{−1} Inductive load coltage V_{L} V = J C^{−1} [M] [L]^{2} [T]^{−3} [I]^{−1} Capacitive reactance X_{C} Ω^{−1} m^{−1} [I]^{2} [T]^{3} [M]^{−2} [L]^{−2} Inductive reactance X_{L} 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, φ dimensionless dimensionless AC peak current I_{0} A [I] AC root mean square current I_{rms} A [I] AC peak voltage V_{0} V = J C^{−1} [M] [L]^{2} [T]^{−3} [I]^{−1} AC root mean square voltage V_{rms} V = J C^{−1} [M] [L]^{2} [T]^{−3} [I]^{−1} AC emf, root mean square V = J C^{−1} [M] [L]^{2} [T]^{−3} [I]^{−1} AC average power W = J s^{−1} [M] [L]^{2} [T]^{−3} Capacitive time constant τ_{C} s [T] Inductive time constant τ_{L} s [T]
Magnetic circuits
Main article: 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 Equations Electric 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 nonuniform fields and dipole moments
Magnetic fields and moments
See also: Magnetic moment
General classical equations

Physical situation Equations Magnetic potential, EM vector potential Due to a magnetic moment Magnetic moment due to a current distribution Magnetostatic torque and potential energy due to nonuniform fields and dipole moments
Electromagnetic induction

Physical situation Nomenclature Equations Transformation of voltage  N = number of turns of conductor
 η = energy efficiency
Electric circuits and electronics
Below N = number of conductors or circuit components. Subcript net refers to the equivalent and resultant property value.

Physical situation Nomenclature Series Parallel Resistors and conductors  R_{i} = resistance of resistor or conductor i
 G_{i} = conductance of conductor or conductor i
Charge, capacitors, currents  q_{i} = capacitance of capacitor i
 q_{i} = charge of charge carrier i
Inductors  L_{i} = selfinductance of inductor i
 L_{ij} = selfinductance element ij of L matrix
 M_{ij} = mutual inductance between inductors i and j

Series circuit equations
Circuit DC Circuit equations AC Circuit equations RC circuits Circuit equation Capacitor charge
Capacitor discharge
RL circuits Circuit equation Inductor current rise
Inductor current fall
LC circuits Circuit equation Circuit equation Circuit resonant frequency
Circuit charge
Circuit current
Circuit electrical potential energy
Circuit magnetic potential energy
RLC Circuits Circuit equation Circuit equation Circuit charge
See also
 SI electromagnetism units
 Defining equation (physical chemistry)
 List of equations in classical mechanics
 Table of thermodynamic equations
 List of equations in wave theory
 List of relativistic equations
 List of equations in fluid mechanics
 List of equations in gravitation
 List of photonics equations
 List of equations in quantum mechanics
 List of equations in nuclear and particle physics
Footnotes
 ^ M. Mansfield, C. O’Sullivan (2011). Understanding Physics (2nd ed.). John Wiley & Sons. ISBN 9780470746370.
Sources
 P.M. Whelan, M.J. Hodgeson (1978). Essential Principles of Physics (2nd ed.). John Murray. ISBN 0719533821.
 G. Woan (2010). The Cambridge Handbook of Physics Formulas. Cambridge University Press. ISBN 9780521575072.
 A. Halpern (1988). 3000 Solved Problems in Physics, Schaum Series. Mc Graw Hill. ISBN 9780070257344.
 R.G. Lerner, G.L. Trigg (2005). Encyclopaedia of Physics (2nd ed.). VHC Publishers, Hans Warlimont, Springer. pp. 12–13. ISBN 9780070257344.
 C.B. Parker (1994). McGraw Hill Encyclopaedia of Physics (2nd ed.). McGraw Hill. ISBN 0070514003.
 P.A. Tipler, G. Mosca (2008). Physics for Scientists and Engineers: With Modern Physics (6th ed.). W.H. Freeman and Co. ISBN 9781429202657.
 L.N. Hand, J.D. Finch (2008). Analytical Mechanics. Cambridge University Press,. ISBN 9780521575720.
 T.B. Arkill, C.J. Millar (1974). Mechanics, Vibrations and Waves. John Murray,. ISBN 0719528828.
 H.J. Pain (1983). The Physics of Vibrations and Waves (3rd ed.). John Wiley & Sons,. ISBN 0471901822.
 J.R. Forshaw, A.G. Smith (2009). Dynamics and Relativity. Wiley,. ISBN 9780470014608.
 G.A.G. Bennet (1974). Electricity and Modern Physics (2nd ed.). Edward Arnold (UK). ISBN 0713124598.
 I.S. Grant, W.R. Phillips, Manchester Physics (2008). Electromagnetism (2nd ed.). John Wiley & Sons. ISBN 9780471927129.
 D.J. Griffiths (2007). Introduction to Electrodynamics (3rd ed.). Pearson Education, Dorling Kindersley,. ISBN 8177582933.
Further reading
 L.H. Greenberg (1978). Physics with Modern Applications. HoltSaunders International W.B. Saunders and Co. ISBN 0721642470.
 J.B. Marion, W.F. Hornyak (1984). Principles of Physics. HoltSaunders International Saunders College. ISBN 4833701952.
 A. Beiser (1987). Concepts of Modern Physics (4th ed.). McGrawHill (International). ISBN 0071001441.
 H.D. Young, R.A. Freedman (2008). University Physics – With Modern Physics (12th ed.). AddisonWesley (Pearson International). ISBN 0321501306.