List of electromagnetism equations

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 and A m. Dimensional analysis shows that magnetic charges relate by q_m = μ₀ q_m.

Initial quantities

Quantity	symbol/s	SI units	Dimension
Electric charge	q_e, q, Q	C = As
Monopole strength, magnetic charge	q_m, g, p	Wb or Am	²⁻² ⁻¹

Electric quantities

Contrary to the strong analogy between gravitation and electrostatics, there are no "centre of charge" or "centre of electrostatic attraction" analogues.
Electric transport

Quantity	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	⁻ⁿ
Capacitance	C	V = voltage, not volume.	F = C V⁻¹	²⁴⁻²⁻¹
Electric current	I		A
Electric current density	J		A m⁻²	⁻²
Displacement current density	J_d		A m⁻²	⁻²
Convection current density	J_c		A m⁻²	⁻²

Electric fields

Quantity	symbol/s	Defining equation	SI units	Dimension
Electric field, field strength, flux density, potential gradient	E		N C⁻¹ = V m⁻¹	⁻³⁻¹
Electric flux	Φ_E		N m² C⁻¹	³⁻³⁻¹
Absolute permittivity;	ε		F m⁻¹	² ⁴ ⁻¹ ⁻³
Electric dipole moment	p	a = charge separation directed from -ve to +ve charge	C m
Electric Polarization, polarization density	P		C m⁻²	⁻²
Electric displacement field, flux density	D		C m⁻²	⁻²
Electric displacement flux	Φ_D		C
Absolute electric potential, EM scalar potential relative to point Theoretical: Practical:	φ,V		V = J C⁻¹	² ⁻³ ⁻¹
Voltage, Electric potential difference	Δφ,ΔV		V = J C⁻¹	² ⁻³ ⁻¹

Magnetic quantities

Magnetic transport

Quantity	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, 2, 3	²⁻² ⁻¹
Monopole current	I_m		Wb s⁻¹ A m s⁻¹	²⁻³ ⁻¹ ⁻¹
Monopole current density	J_m		Wb s⁻¹ m⁻² A m⁻¹ s⁻¹	⁻³ ⁻¹ ⁻¹⁻¹

Magnetic fields

Quantity	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	⁻²⁻¹
Magnetic potential, EM vector potential	A		T m = N A⁻¹ = Wb m³	⁻²⁻¹
Magnetic flux	Φ_B		Wb = T m²	²⁻²⁻¹
Magnetic permeability			V·s·A⁻¹·m⁻¹ = N·A⁻² = T·m·A⁻¹ = Wb·A⁻¹·m⁻¹	⁻²⁻²
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 m²	²
Magnetization	M		A m⁻¹	⁻¹
Magnetic field intensity,	H	Two definitions are possible: most common: using pole strengths,	A m⁻¹	⁻¹
Intensity of magnetization, magnetic polarization	I, J		T = N A⁻¹ m⁻¹ = Wb m⁻²	⁻²⁻¹
Self Inductance	L	Two equivalent definitions are possible:	H = Wb A⁻¹	² ⁻² ⁻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	² ⁻² ⁻²
Gyromagnetic ratio	γ		Hz T⁻¹	⁻¹

Electric circuits

DC circuits, general definitions

Quantity	symbol/s	Defining equation	SI units	Dimension
Terminal Voltage for power supply	V_ter		V = J C⁻¹	² ⁻³ ⁻¹
Load Voltage for Circuit	V_load		V = J C⁻¹	² ⁻³ ⁻¹
Internal resistance of power supply	R_int		Ω = V A⁻¹ = J s C⁻²	² ⁻³ ⁻²
Load resistance of circuit	R_ext		Ω = V A⁻¹ = J s C⁻²	² ⁻³ ⁻²
Electromotive force, voltage across entire circuit including power supply, external components and conductors	E		V = J C⁻¹	² ⁻³ ⁻¹

AC circuits

Quantity	symbol/s	Defining equation	SI units	Dimension
Resistive load voltage	V_R		V = J C⁻¹	² ⁻³ ⁻¹
Capacitive load voltage	V_C		V = J C⁻¹	² ⁻³ ⁻¹
Inductive load voltage	V_L		V = J C⁻¹	² ⁻³ ⁻¹
Capacitive reactance	X_C		Ω⁻¹ m⁻¹	² ³ ⁻² ⁻²
Inductive reactance	X_L		Ω⁻¹ m⁻¹	² ³ ⁻² ⁻²
AC electrical impedance	Z		Ω⁻¹ m⁻¹	² ³ ⁻² ⁻²
Phase constant	δ, φ		dimensionless	dimensionless
AC peak current	I₀		A
AC root mean square current	I_rms		A
AC peak voltage	V₀		V = J C⁻¹	² ⁻³ ⁻¹
AC root mean square voltage	V_rms		V = J C⁻¹	² ⁻³ ⁻¹
AC emf, root mean square			V = J C⁻¹	² ⁻³ ⁻¹
AC average power			W = J s⁻¹	² ⁻³
Capacitive time constant	τ_C		s
Inductive time constant	τ_L		s

Magnetic circuits

Quantity	symbol/s	Defining equation	SI units	Dimension
Magnetomotive force, mmf	F,	N = number of turns of conductor	A

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 non-uniform fields and dipole moments

Magnetic fields and moments

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 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	Parallel
Resistors and conductors	R_i = resistance of resistor or conductor i G_i = conductance of resistor or conductor i
Charge, capacitors, currents	C_i = capacitance of capacitor i q_i = charge of charge carrier i
Inductors	L_i = self-inductance of inductor i L_ij = self-inductance element ij of L matrix M_ij = mutual inductance between inductors i and j