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

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
V = voltage, not volume.F = C V⁻¹²⁴⁻²⁻¹Electric currentIAElectric current densityJA m⁻²⁻²Displacement current densityJ_dA m⁻²⁻²Convection current densityJ_cA m⁻²⁻²
Electric fields
a = charge separation
directed from -ve to +ve chargeC mElectric Polarization, polarization densityPC m⁻²⁻²Electric displacement fieldDC m⁻²⁻²Electric displacement fluxΦ_DCAbsolute electric potential, EM scalar potential relative to point
Theoretical:

Practical:
φ,VV = J C⁻¹ ² ⁻³ ⁻¹Voltage, Electric potential differenceΔφ,ΔVV = J C⁻¹ ² ⁻³ ⁻¹

Magnetic quantities

Magnetic transport
A m,

n = 1, 2, 3²⁻² ⁻¹

Monopole currentI_mWb s⁻¹

A m s⁻¹²⁻³ ⁻¹

⁻¹ Monopole current densityJ_mWb s⁻¹ m⁻²

A m⁻¹ s⁻¹⁻³ ⁻¹

⁻¹⁻¹
Magnetic fields
Two definitions are possible:
using pole strengths,

using currents:

a = pole separation
N is the number of turns of conductorA m²²MagnetizationMA m⁻¹ ⁻¹Magnetic field intensity, HTwo definitions are possible:
most common:

using pole strengths,
A m⁻¹ ⁻¹Intensity of magnetization, magnetic polarizationI, JT = N A⁻¹ m⁻¹ = Wb m²⁻²⁻¹Self InductanceLTwo equivalent definitions are possible:H = Wb A⁻¹² ⁻² ⁻²Mutual inductanceMAgain 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⁻¹² ⁻² ⁻²Gyromagnetic ratio γHz T⁻¹⁻¹

Electric circuits

DC circuits, general definitions
Power SupplyV_terV = J C⁻¹ ² ⁻³ ⁻¹Load Voltage for CircuitV_loadV = J C⁻¹ ² ⁻³ ⁻¹Internal resistance of power supplyR_intΩ = V A⁻¹ = J s C⁻²² ⁻³ ⁻²Load resistance of circuitR_extΩ = V A⁻¹ = J s C⁻²² ⁻³ ⁻²Electromotive force, voltage across entire circuit including power supply, external components and conductorsEV = J C⁻¹ ² ⁻³ ⁻¹
AC circuits

Magnetic circuits

N = number of turns of conductorA

Electromagnetism

Electric fields

General Classical Equations

Magnetic fields and moments

General classical equations

Electromagnetic induction

N = number of turns of conductor
η = energy efficiency