List of electromagnetism equations

This article summarizes equations in the theory of electromagnetism.

Contents

DefinitionsEdit

 
Lorentz force on a charged particle (of charge q) in motion (velocity v), used as the definition of the E field and B field.

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 quantitiesEdit

Quantity (common name/s) (Common) symbol/s SI units Dimension
Electric 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 quantitiesEdit

 
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal , d is the dipole moment between two point charges, the volume density of these is the polarization density P. Position vector r is a point to calculate the electric field; r′ is a point in the charged object.

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 mn, n = 1, 2, 3 [I][T][L]n
Capacitance C  

V = 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]−2
Displacement current density Jd   A m−2 [I][L]−2
Convection current density Jc   A m−2 [I][L]−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 ΦE   N m2 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 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]−1
Voltage, Electric potential difference ΔφV   V = J C−1 [M] [L]2 [T]−3 [I]−1

Magnetic quantitiesEdit

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 mn

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 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 m3 [M][L][T]−2[I]−1
Magnetic flux ΦB   Wb = T m2 [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, μB, Π

Two definitions are possible:

using pole strengths,
 

using currents:
 

a = pole separation

N is the number of turns of conductor

A m2 [I][L]2
Magnetization M   A m−1 [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 m2 [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]−2
Gyromagnetic ratio (for charged particles in a magnetic field) γ   Hz T−1 [M]−1[T][I]

Electric circuitsEdit

DC circuits, general definitions

Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension
Terminal Voltage for

Power Supply

Vter V = J C−1 [M] [L]2 [T]−3 [I]−1
Load Voltage for Circuit Vload V = J C−1 [M] [L]2 [T]−3 [I]−1
Internal resistance of power supply Rint   Ω = V A−1 = J s C−2 [M][L]2 [T]−3 [I]−2
Load resistance of circuit Rext   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 VR   V = J C−1 [M] [L]2 [T]−3 [I]−1
Capacitive load voltage VC   V = J C−1 [M] [L]2 [T]−3 [I]−1
Inductive load voltage VL   V = J C−1 [M] [L]2 [T]−3 [I]−1
Capacitive reactance XC   Ω−1 m−1 [I]2 [T]3 [M]−2 [L]−2
Inductive reactance XL   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 I0   A [I]
AC root mean square current Irms   A [I]
AC peak voltage V0   V = J C−1 [M] [L]2 [T]−3 [I]−1
AC root mean square voltage Vrms   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 τC   s [T]
Inductive time constant τL   s [T]

Magnetic circuitsEdit

Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension
Magnetomotive force, mmf F,    

N = number of turns of conductor

A [I]

ElectromagnetismEdit

Electric fieldsEdit

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 momentsEdit

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  

 

Electromagnetic inductionEdit

Physical situation Nomenclature Equations
Transformation of voltage
  • N = number of turns of conductor
  • η = energy efficiency
 

Electric circuits and electronicsEdit

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
  • Ri = 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 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 alsoEdit

FootnotesEdit

  1. ^ M. Mansfield; C. O'Sullivan (2011). Understanding Physics (2nd ed.). John Wiley & Sons. ISBN 978-0-470-74637-0.

SourcesEdit

  • P.M. Whelan; M.J. Hodgeson (1978). Essential Principles of Physics (2nd ed.). John Murray. ISBN 0-7195-3382-1.
  • G. Woan (2010). The Cambridge Handbook of Physics Formulas. Cambridge University Press. ISBN 978-0-521-57507-2.
  • A. Halpern (1988). 3000 Solved Problems in Physics, Schaum Series. Mc Graw Hill. ISBN 978-0-07-025734-4.
  • R.G. Lerner; G.L. Trigg (2005). Encyclopaedia of Physics (2nd ed.). VHC Publishers, Hans Warlimont, Springer. pp. 12–13. ISBN 978-0-07-025734-4.
  • C.B. Parker (1994). McGraw Hill Encyclopaedia of Physics (2nd ed.). McGraw Hill. ISBN 0-07-051400-3.
  • P.A. Tipler; G. Mosca (2008). Physics for Scientists and Engineers: With Modern Physics (6th ed.). W.H. Freeman and Co. ISBN 978-1-4292-0265-7.
  • L.N. Hand; J.D. Finch (2008). Analytical Mechanics. Cambridge University Press. ISBN 978-0-521-57572-0.
  • T.B. Arkill; C.J. Millar (1974). Mechanics, Vibrations and Waves. John Murray. ISBN 0-7195-2882-8.
  • H.J. Pain (1983). The Physics of Vibrations and Waves (3rd ed.). John Wiley & Sons. ISBN 0-471-90182-2.
  • J.R. Forshaw; A.G. Smith (2009). Dynamics and Relativity. Wiley. ISBN 978-0-470-01460-8.
  • G.A.G. Bennet (1974). Electricity and Modern Physics (2nd ed.). Edward Arnold (UK). ISBN 0-7131-2459-8.
  • I.S. Grant; W.R. Phillips; Manchester Physics (2008). Electromagnetism (2nd ed.). John Wiley & Sons. ISBN 978-0-471-92712-9.
  • D.J. Griffiths (2007). Introduction to Electrodynamics (3rd ed.). Pearson Education, Dorling Kindersley. ISBN 81-7758-293-3.

Further readingEdit

  • L.H. Greenberg (1978). Physics with Modern Applications. Holt-Saunders International W.B. Saunders and Co. ISBN 0-7216-4247-0.
  • J.B. Marion; W.F. Hornyak (1984). Principles of Physics. Holt-Saunders International Saunders College. ISBN 4-8337-0195-2.
  • A. Beiser (1987). Concepts of Modern Physics (4th ed.). McGraw-Hill (International). ISBN 0-07-100144-1.
  • H.D. Young; R.A. Freedman (2008). University Physics – With Modern Physics (12th ed.). Addison-Wesley (Pearson International). ISBN 0-321-50130-6.