List of electromagnetism equations

Electromagnetism

* Electricity
* Magnetism
* Optics
* History
* Computational
* Textbooks
* Phenomena

Electrostatics

* Charge density
* Conductor
* Coulomb law
* Electret
* Electric charge
* Electric dipole
* Electric field
* Electric flux
* Electric potential
* Electrostatic discharge
* Electrostatic induction
* Gauss's law
* Insulator
* Permittivity
* Polarization
* Potential energy
* Static electricity
* Triboelectricity

Magnetostatics

* Ampère's law
* Biot–Savart law
* Gauss's law for magnetism
* Magnetic dipole
* Magnetic field
* Magnetic flux
* Magnetic scalar potential
* Magnetic vector potential
* Magnetization
* Permeability
* Right-hand rule

Electrodynamics

* Bremsstrahlung
* Cyclotron radiation
* Displacement current
* Eddy current
* Electromagnetic field
* Electromagnetic induction
* Electromagnetic pulse
* Electromagnetic radiation
* Faraday's law
* Jefimenko equations
* Larmor formula
* Lenz's law
* Liénard–Wiechert potential
* London equations
* Lorentz force
* Maxwell's equations
* Maxwell tensor
* Poynting vector
* Synchrotron radiation

Electrical network

* Alternating current
* Capacitance
* Current density
* Direct current
* Electric current
* Electric power
* Electrolysis
* Electromotive force
* Impedance
* Inductance
* Joule heating
* Kirchhoff's laws
* Network analysis
* Ohm's law
* Parallel circuit
* Resistance
* Resonant cavities
* Series circuit
* Voltage
* Watt
* Waveguides

Magnetic circuit

* AC motor
* DC motor
* Electric machine
* Electric motor
* Gyrator–capacitor
* Induction motor
* Linear motor
* Magnetomotive force
* Permeance
* Reluctance (complex)
* Reluctance (real)
* Rotor
* Stator
* Transformer

Covariant formulation

* Electromagnetic tensor
* Electromagnetism and special relativity
* Four-current
* Four-potential
* Mathematical descriptions
* Maxwell equations in curved spacetime
* Relativistic electromagnetism
* Stress–energy tensor

Scientists

* Ampère
* Biot
* Coulomb
* Davy
* Einstein
* Faraday
* Fizeau
* Gauss
* Heaviside
* Helmholtz
* Henry
* Hertz
* Hopkinson
* Jefimenko
* Joule
* Kelvin
* Kirchhoff
* Larmor
* Lenz
* Liénard
* Lorentz
* Maxwell
* Neumann
* Ohm
* Ørsted
* Poisson
* Poynting
* Ritchie
* Savart
* Singer
* Steinmetz
* Tesla
* Thomson
* Volta
* Weber
* Wiechert

* v
* t
* e

This article summarizes equations in the theory of electromagnetism.

## Definitions

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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 quantities

[edit]

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

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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 quantities

[edit]

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 n̂, 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.[citation needed]

Electric transport

Quantity (common name/s)  | (Common) symbol/s  | Defining equation  | SI units  | Dimension

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Linear, surface, volumetric charge density  | λe for Linear, σe for surface, ρe for volume.  |  q e = ∫ λ e d ℓ {\displaystyle q_{e}=\int \lambda _{e}\mathrm {d} \ell }

q e = ∬ σ e d S {\displaystyle q_{e}=\iint \sigma _{e}\mathrm {d} S}

q e = ∭ ρ e d V {\displaystyle q_{e}=\iiint \rho _{e}\mathrm {d} V}

| C m−n, n = 1, 2, 3  | [I][T][L]−n
Capacitance | C |  C = d q d V {\displaystyle C={\mathrm {d} q \over \mathrm {d} V}\,\\!}

V = voltage, not volume.

| F = C V−1 | [I]2[T]4[L]−2[M]−1
Electric current | I |  I = d q d t {\displaystyle I={\mathrm {d} q \over \mathrm {d} t}\,\\!} | A  | [I]
Electric current density | J |  I = J ⋅ d S {\displaystyle I=\mathbf {J} \cdot \mathrm {d} \mathbf {S} } | A m−2 | [I][L]−2
Displacement current density  | Jd |  J d = ∂ D ∂ t = ε 0 ( ∂ E ∂ t ) {\displaystyle \mathbf {J} _{\mathrm {d} }={\partial \mathbf {D} \over \partial t}=\varepsilon _{0}\left({\partial \mathbf {E} \over \partial t}\right)\,\\!} | A m−2 | [I][L]−2
Convection current density  | Jc |  J c = ρ v {\displaystyle \mathbf {J} _{\mathrm {c} }=\rho \mathbf {v} \,\\!} | A m−2 | [I][L]−2

Electric fields

Quantity (common name/s)  | (Common) symbol/s  | Defining equation  | SI units  | Dimension

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Electric field, field strength, flux density, potential gradient  | E |  E = F q {\displaystyle \mathbf {E} ={\mathbf {F} \over q}\,\\!} | N C−1 = V m−1 | [M][L][T]−3[I]−1
Electric flux | ΦE |  Φ E = ∫ S E ⋅ d A {\displaystyle \Phi _{E}=\int _{S}\mathbf {E} \cdot \mathrm {d} \mathbf {A} \,\\!} | N m2 C−1 | [M][L]3[T]−3[I]−1
Absolute permittivity;  | ε |  ε = ε r ε 0 {\displaystyle \varepsilon =\varepsilon _{r}\varepsilon _{0}\,\\!} | F m−1 | [I]2 [T]4 [M]−1 [L]−3
Electric dipole moment | p |  p = q a {\displaystyle \mathbf {p} =q\mathbf {a} \,\\!}

a = charge separation directed from -ve to +ve charge

| C m  | [I][T][L]
Electric Polarization, polarization density | P |  P = d ⟨ p ⟩ d V {\displaystyle \mathbf {P} ={\mathrm {d} \langle \mathbf {p} \rangle \over \mathrm {d} V}\,\\!} | C m−2 | [I][T][L]−2
Electric displacement field, flux density  | D |  D = ε E = ε 0 E + P {\displaystyle \mathbf {D} =\varepsilon \mathbf {E} =\varepsilon _{0}\mathbf {E} +\mathbf {P} \,} | C m−2 | [I][T][L]−2
Electric displacement flux  | ΦD |  Φ D = ∫ S D ⋅ d A {\displaystyle \Phi _{D}=\int _{S}\mathbf {D} \cdot \mathrm {d} \mathbf {A} \,\\!} | C  | [I][T]
Absolute electric potential, EM scalar potential relative to point  r 0 {\displaystyle r_{0}\,\\!}

Theoretical:  r 0 = ∞ {\displaystyle r_{0}=\infty \,\\!}
Practical:  r 0 = R e a r t h {\displaystyle r_{0}=R_{\mathrm {earth} }\,\\!} (Earth's radius)

| φ ,V |  V = − W ∞ r q = − 1 q ∫ ∞ r F ⋅ d r = − ∫ r 1 r 2 E ⋅ d r {\displaystyle V=-{\frac {W_{\infty r}}{q}}=-{\frac {1}{q}}\int _{\infty }^{r}\mathbf {F} \cdot \mathrm {d} \mathbf {r} =-\int _{r_{1}}^{r_{2}}\mathbf {E} \cdot \mathrm {d} \mathbf {r} \,\\!} | V = J C−1 | [M] [L]2 [T]−3 [I]−1
Voltage, Electric potential difference  | Δφ,ΔV |  Δ V = − Δ W q = − 1 q ∫ r 1 r 2 F ⋅ d r = − ∫ r 1 r 2 E ⋅ d r {\displaystyle \Delta V=-{\frac {\Delta W}{q}}=-{\frac {1}{q}}\int _{r_{1}}^{r_{2}}\mathbf {F} \cdot \mathrm {d} \mathbf {r} =-\int _{r_{1}}^{r_{2}}\mathbf {E} \cdot \mathrm {d} \mathbf {r} \,\\!} | V = J C−1 | [M] [L]2 [T]−3 [I]−1

### Magnetic quantities

[edit]

Magnetic transport

Quantity (common name/s)  | (Common) symbol/s  | Defining equation  | SI units  | Dimension

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Linear, surface, volumetric pole density  | λm for Linear, σm for surface, ρm for volume.  |  q m = ∫ λ m d ℓ {\displaystyle q_{m}=\int \lambda _{m}\mathrm {d} \ell }

q m = ∬ σ m d S {\displaystyle q_{m}=\iint \sigma _{m}\mathrm {d} S}

q m = ∭ ρ m d V {\displaystyle q_{m}=\iiint \rho _{m}\mathrm {d} V}

| 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 |  I m = d q m d t {\displaystyle I_{m}={\mathrm {d} q_{m} \over \mathrm {dt} }\,\\!} | Wb s−1

A m s−1

| [L]2[M][T]−3 [I]−1 (Wb)

[I][L][T]−1 (Am)

Monopole current density  | Jm |  I = ∬ J m ⋅ d A {\displaystyle I=\iint \mathbf {J} _{\mathrm {m} }\cdot \mathrm {d} \mathbf {A} } | 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

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Magnetic field, field strength, flux density, induction field  | B |  F = q e ( v × B ) {\displaystyle \mathbf {F} =q_{e}\left(\mathbf {v} \times \mathbf {B} \right)\,\\!} | T = N A−1 m−1 = Wb m−2 | [M][T]−2[I]−1
Magnetic potential, EM vector potential  | A |  B = ∇ × A {\displaystyle \mathbf {B} =\nabla \times \mathbf {A} } | T m = N A−1 = Wb m3 | [M][L][T]−2[I]−1
Magnetic flux | ΦB |  Φ B = ∫ S B ⋅ d A {\displaystyle \Phi _{B}=\int _{S}\mathbf {B} \cdot \mathrm {d} \mathbf {A} \,\\!} | Wb = T m2 | [L]2[M][T]−2[I]−1
Magnetic permeability |  μ {\displaystyle \mu \,\\!} |  μ = μ r μ 0 {\displaystyle \mu \ =\mu _{r}\,\mu _{0}\,\\!} | 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,
m = q m a {\displaystyle \mathbf {m} =q_{m}\mathbf {a} \,\\!}

using currents:
m = N I A n ^ {\displaystyle \mathbf {m} =NIA\mathbf {\hat {n}} \,\\!}

a = pole separation

N is the number of turns of conductor

| A m2 | [I][L]2
Magnetization | M |  M = d ⟨ m ⟩ d V {\displaystyle \mathbf {M} ={\mathrm {d} \langle \mathbf {m} \rangle \over \mathrm {d} V}\,\\!} | A m−1 | [I] [L]−1
Magnetic field intensity, (AKA field strength)  | H | Two definitions are possible:

most common:
B = μ H = μ 0 ( H + M ) {\displaystyle \mathbf {B} =\mu \mathbf {H} =\mu _{0}\left(\mathbf {H} +\mathbf {M} \right)\,}

using pole strengths,[1]
H = F q m {\displaystyle \mathbf {H} ={\mathbf {F} \over q_{m}}\,}

| A m−1 | [I] [L]−1
Intensity of magnetization, magnetic polarization  | I, J |  I = μ 0 M {\displaystyle \mathbf {I} =\mu _{0}\mathbf {M} \,\\!} | T = N A−1 m−1 = Wb m−2 | [M][T]−2[I]−1
Self Inductance | L | Two equivalent definitions are possible:

L = N ( d Φ d I ) {\displaystyle L=N\left({\mathrm {d} \Phi \over \mathrm {d} I}\right)\,\\!}

L ( d I d t ) = − N V {\displaystyle L\left({\mathrm {d} I \over \mathrm {d} t}\right)=-NV\,\\!}

| H = Wb A−1 | [L]2 [M] [T]−2 [I]−2
Mutual inductance | M | Again two equivalent definitions are possible:

M 1 = N ( d Φ 2 d I 1 ) {\displaystyle M_{1}=N\left({\mathrm {d} \Phi _{2} \over \mathrm {d} I_{1}}\right)\,\\!}

M ( d I 2 d t ) = − N V 1 {\displaystyle M\left({\mathrm {d} I_{2} \over \mathrm {d} t}\right)=-NV_{1}\,\\!}

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;

M 2 = N ( d Φ 1 d I 2 ) {\displaystyle M_{2}=N\left({\mathrm {d} \Phi _{1} \over \mathrm {d} I_{2}}\right)\,\\!}
M ( d I 1 d t ) = − N V 2 {\displaystyle M\left({\mathrm {d} I_{1} \over \mathrm {d} t}\right)=-NV_{2}\,\\!}

| H = Wb A−1 | [L]2 [M] [T]−2 [I]−2
Gyromagnetic ratio (for charged particles in a magnetic field)  | γ |  ω = γ B {\displaystyle \omega =\gamma B\,\\!} | Hz T−1 | [M]−1[T][I]

### Electric circuits

[edit]

DC circuits, general definitions

Main article: Direct current

Quantity (common name/s)  | (Common) symbol/s  | Defining equation  | SI units  | Dimension

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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 |  R i n t = V t e r I {\displaystyle R_{\mathrm {int} }={V_{\mathrm {ter} } \over I}\,\\!} | Ω = V A−1 = J s C−2 | [M][L]2 [T]−3 [I]−2
Load resistance of circuit  | Rext |  R e x t = V l o a d I {\displaystyle R_{\mathrm {ext} }={V_{\mathrm {load} } \over I}\,\\!} | 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 |  E = V t e r + V l o a d {\displaystyle {\mathcal {E}}=V_{\mathrm {ter} }+V_{\mathrm {load} }\,\\!} | V = J C−1 | [M] [L]2 [T]−3 [I]−1

AC circuits

Main articles: Alternating current and Resonance

Quantity (common name/s)  | (Common) symbol/s  | Defining equation  | SI units  | Dimension

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Resistive load voltage  | VR |  V R = I R R {\displaystyle V_{R}=I_{R}R\,\\!} | V = J C−1 | [M] [L]2 [T]−3 [I]−1
Capacitive load voltage  | VC |  V C = I C X C {\displaystyle V_{C}=I_{C}X_{C}\,\\!} | V = J C−1 | [M] [L]2 [T]−3 [I]−1
Inductive load voltage  | VL |  V L = I L X L {\displaystyle V_{L}=I_{L}X_{L}\,\\!} | V = J C−1 | [M] [L]2 [T]−3 [I]−1
Capacitive reactance | XC |  X C = 1 ω d C {\displaystyle X_{C}={\frac {1}{\omega _{\mathrm {d} }C}}\,\\!} | Ω−1 m−1 | [I]2 [T]3 [M]−2 [L]−2
Inductive reactance | XL |  X L = ω d L {\displaystyle X_{L}=\omega _{d}L\,\\!} | Ω−1 m−1 | [I]2 [T]3 [M]−2 [L]−2
AC electrical impedance | Z |  V = I Z {\displaystyle V=IZ\,\\!}

Z = R 2 + ( X L − X C ) 2 {\displaystyle Z={\sqrt {R^{2}+\left(X_{L}-X_{C}\right)^{2}}}\,\\!}

| Ω−1 m−1 | [I]2 [T]3 [M]−2 [L]−2
Phase constant  | δ, φ |  tan ⁡ ϕ = X L − X C R {\displaystyle \tan \phi ={\frac {X_{L}-X_{C}}{R}}\,\\!} | dimensionless  | dimensionless
AC peak current  | I0 |  I 0 = I r m s 2 {\displaystyle I_{0}=I_{\mathrm {rms} }{\sqrt {2}}\,\\!} | A  | [I]
AC root mean square current  | Irms |  I r m s = 1 T ∫ 0 T [ I ( t ) ] 2 d t {\displaystyle I_{\mathrm {rms} }={\sqrt {{\frac {1}{T}}\int _{0}^{T}\left[I\left(t\right)\right]^{2}\mathrm {d} t}}\,\\!} | A  | [I]
AC peak voltage  | V0 |  V 0 = V r m s 2 {\displaystyle V_{0}=V_{\mathrm {rms} }{\sqrt {2}}\,\\!} | V = J C−1 | [M] [L]2 [T]−3 [I]−1
AC root mean square voltage  | Vrms |  V r m s = 1 T ∫ 0 T [ V ( t ) ] 2 d t {\displaystyle V_{\mathrm {rms} }={\sqrt {{\frac {1}{T}}\int _{0}^{T}\left[V\left(t\right)\right]^{2}\mathrm {d} t}}\,\\!} | V = J C−1 | [M] [L]2 [T]−3 [I]−1
AC emf, root mean square  |  E r m s , ⟨ E ⟩ {\displaystyle {\mathcal {E}}_{\mathrm {rms} },{\sqrt {\langle {\mathcal {E}}\rangle }}\,\\!} |  E r m s = E m / 2 {\displaystyle {\mathcal {E}}_{\mathrm {rms} }={\mathcal {E}}_{\mathrm {m} }/{\sqrt {2}}\,\\!} | V = J C−1 | [M] [L]2 [T]−3 [I]−1
AC average power  |  ⟨ P ⟩ {\displaystyle \langle P\rangle \,\\!} |  ⟨ P ⟩ = E I r m s cos ⁡ ϕ {\displaystyle \langle P\rangle ={\mathcal {E}}I_{\mathrm {rms} }\cos \phi \,\\!} | W = J s−1 | [M] [L]2 [T]−3
Capacitive time constant  | τC |  τ C = R C {\displaystyle \tau _{C}=RC\,\\!} | s  | [T]
Inductive time constant  | τL |  τ L = L R {\displaystyle \tau _{L}={L \over R}\,\\!} | s  | [T]

### Magnetic circuits

[edit]

Main article: Magnetic circuits

Quantity (common name/s)  | (Common) symbol/s  | Defining equation  | SI units  | Dimension

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Magnetomotive force, mmf  | F,  F , M {\displaystyle {\mathcal {F}},{\mathcal {M}}} |  M = N I {\displaystyle {\mathcal {M}}=NI}

N = number of turns of conductor

| A  | [I]

## Electromagnetism

[edit]

### Electric fields

[edit]

Summary of electrostatic relations between electric potential, electric field and charge density. Here,  r = x − x ′ {\displaystyle \mathbf {r} =\mathbf {x} -\mathbf {x'} } .

General Classical Equations

Physical situation  | Equations

|

Electric potential gradient and field  |  E = − ∇ V {\displaystyle \mathbf {E} =-\nabla V}

Δ V = − ∫ r 1 r 2 E ⋅ d r {\displaystyle \Delta V=-\int _{r_{1}}^{r_{2}}\mathbf {E} \cdot d\mathbf {r} \,\\!}

Point charge  |  E ( r ) = q 4 π ε 0 r ^ | r | 2 = q 4 π ε 0 r | r | 3 {\displaystyle \mathbf {E} (\mathbf {r} )={q \over 4\pi \varepsilon _{0}}{{\hat {\mathbf {r} }} \over {|\mathbf {r} |}^{2}}={q \over 4\pi \varepsilon _{0}}{\mathbf {r} \over {|\mathbf {r} |}^{3}}\,\\!}
At a point in a local array of point charges  |  E ( r ) = 1 4 π ε 0 ∑ i = 1 n q i r ^ i | r i − r | 2 = 1 4 π ε 0 ∑ i = 1 n q i r i | r i − r | 3 {\displaystyle \mathbf {E} (\mathbf {r} )={1 \over 4\pi \varepsilon _{0}}\sum _{i=1}^{n}q_{i}{{\hat {\mathbf {r} }}_{i} \over {|\mathbf {r_{i}-r} |}^{2}}={1 \over 4\pi \varepsilon _{0}}\sum _{i=1}^{n}q_{i}{\mathbf {r} _{i} \over {|\mathbf {r_{i}-r} |}^{3}}}
At a point due to a continuum of charge  |  E ( r ) = 1 4 π ε 0 ∭ ρ ( r ′ ) r ′ | r ′ | 3 d 3 | r ′ | {\displaystyle \mathbf {E} (\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}\iiint \,\rho (\mathbf {r} '){\mathbf {r} ' \over {|\mathbf {r} '|}^{3}}\mathrm {d} ^{3}|\mathbf {r} '|}
Electrostatic torque and potential energy due to non-uniform fields and dipole moments  |  τ = ∫ V d p × E {\displaystyle {\boldsymbol {\tau }}=\int _{V}\mathrm {d} \mathbf {p} \times \mathbf {E} }

U = − ∫ V d p ⋅ E {\displaystyle U=-\int _{V}\mathrm {d} \mathbf {p} \cdot \mathbf {E} }

### Magnetic fields and moments

[edit]

See also: Magnetic moment

Summary of magnetostatic relations between magnetic vector potential, magnetic field and current density. Here,  r = x − x ′ {\displaystyle \mathbf {r} =\mathbf {x} -\mathbf {x'} } .

General classical equations

Physical situation  | Equations

|

Magnetic potential, EM vector potential  |  B = ∇ × A {\displaystyle \mathbf {B} =\nabla \times \mathbf {A} }
Due to a magnetic moment  |  A = μ 0 4 π m × r | r | 3 {\displaystyle \mathbf {A} ={\frac {\mu _{0}}{4\pi }}{\frac {\mathbf {m} \times \mathbf {r} }{\left|\mathbf {r} \right|^{3}}}}

B ( r ) = ∇ × A = μ 0 4 π ( 3 r ( m ⋅ r ) | r | 5 − m | r | 3 ) {\displaystyle \mathbf {B} ({\mathbf {r} })=\nabla \times {\mathbf {A} }={\frac {\mu _{0}}{4\pi }}\left({\frac {3\mathbf {r} (\mathbf {m} \cdot \mathbf {r} )}{\left|\mathbf {r} \right|^{5}}}-{\frac {\mathbf {m} }{\left|\mathbf {r} \right|^{3}}}\right)}

Magnetic moment due to a current distribution  |  m = 1 2 ∫ V r × J d V {\displaystyle \mathbf {m} ={\frac {1}{2}}\int _{V}\mathbf {r} \times \mathbf {J} \mathrm {d} V}
Magnetostatic torque and potential energy due to non-uniform fields and dipole moments  |  τ = ∫ V d m × B {\displaystyle {\boldsymbol {\tau }}=\int _{V}\mathrm {d} \mathbf {m} \times \mathbf {B} }

U = − ∫ V d m ⋅ B {\displaystyle U=-\int _{V}\mathrm {d} \mathbf {m} \cdot \mathbf {B} }

## Electric circuits and electronics

[edit]

Below N = number of conductors or circuit components. Subscript net refers to the equivalent and resultant property value.

Physical situation  | Nomenclature  | Series  | Parallel

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Resistors and conductors  |

* Ri = resistance of resistor or conductor i
* Gi = conductance of resistor or conductor i

|  R n e t = ∑ i = 1 N R i {\displaystyle R_{\mathrm {net} }=\sum _{i=1}^{N}R_{i}\,\\!}

1 G n e t = ∑ i = 1 N 1 G i {\displaystyle {1 \over G_{\mathrm {net} }}=\sum _{i=1}^{N}{1 \over G_{i}}\,\\!}

|  1 R n e t = ∑ i = 1 N 1 R i {\displaystyle {1 \over R_{\mathrm {net} }}=\sum _{i=1}^{N}{1 \over R_{i}}\,\\!}

G n e t = ∑ i = 1 N G i {\displaystyle G_{\mathrm {net} }=\sum _{i=1}^{N}G_{i}\,\\!}

Charge, capacitors, currents  |

* Ci = capacitance of capacitor i
* qi = charge of charge carrier i

|  q n e t = ∑ i = 1 N q i {\displaystyle q_{\mathrm {net} }=\sum _{i=1}^{N}q_{i}\,\\!}

1 C n e t = ∑ i = 1 N 1 C i {\displaystyle {1 \over C_{\mathrm {net} }}=\sum _{i=1}^{N}{1 \over C_{i}}\,\\!} I n e t = I i {\displaystyle I_{\mathrm {net} }=I_{i}\,\\!}

|  q n e t = ∑ i = 1 N q i {\displaystyle q_{\mathrm {net} }=\sum _{i=1}^{N}q_{i}\,\\!}

C n e t = ∑ i = 1 N C i {\displaystyle C_{\mathrm {net} }=\sum _{i=1}^{N}C_{i}\,\\!} I n e t = ∑ i = 1 N I i {\displaystyle I_{\mathrm {net} }=\sum _{i=1}^{N}I_{i}\,\\!}

Inductors  |

* Li = self-inductance of inductor i
* Lij = self-inductance element ij of L matrix
* Mij = mutual inductance between inductors i and j

|  L n e t = ∑ i = 1 N L i {\displaystyle L_{\mathrm {net} }=\sum _{i=1}^{N}L_{i}\,\\!} |  1 L n e t = ∑ i = 1 N 1 L i {\displaystyle {1 \over L_{\mathrm {net} }}=\sum _{i=1}^{N}{1 \over L_{i}}\,\\!}

V i = ∑ j = 1 N L i j d I j d t {\displaystyle V_{i}=\sum _{j=1}^{N}L_{ij}{\frac {\mathrm {d} I_{j}}{\mathrm {d} t}}\,\\!}

Circuit  | DC Circuit equations  | AC Circuit equations

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|

Series circuit equations  RC circuits | Circuit equation

R d q d t + q C = E {\displaystyle R{\mathrm {d} q \over \mathrm {d} t}+{q \over C}={\mathcal {E}}\,\\!}

Capacitor charge  q = C E ( 1 − e − t / R C ) {\displaystyle q=C{\mathcal {E}}\left(1-e^{-t/RC}\right)\,\\!}

Capacitor discharge  q = C E e − t / R C {\displaystyle q=C{\mathcal {E}}e^{-t/RC}\,\\!}

RL circuits | Circuit equation

L d I d t + R I = E {\displaystyle L{\mathrm {d} I \over \mathrm {d} t}+RI={\mathcal {E}}\,\\!}

Inductor current rise  I = E R ( 1 − e − R t / L ) {\displaystyle I={\frac {\mathcal {E}}{R}}\left(1-e^{-Rt/L}\right)\,\\!}

Inductor current fall  I = E R e − t / τ L = I 0 e − R t / L {\displaystyle I={\frac {\mathcal {E}}{R}}e^{-t/\tau _{L}}=I_{0}e^{-Rt/L}\,\\!}

LC circuits | Circuit equation

L d 2 q d t 2 + q C = E {\displaystyle L{\mathrm {d} ^{2}q \over \mathrm {d} t^{2}}+{q \over C}={\mathcal {E}}\,\\!}

| Circuit equation

L d 2 q d t 2 + q C = E sin ⁡ ( ω 0 t + ϕ ) {\displaystyle L{\mathrm {d} ^{2}q \over \mathrm {d} t^{2}}+{q \over C}={\mathcal {E}}\sin \left(\omega _{0}t+\phi \right)\,\\!}

Circuit resonant frequency  ω r e s = 1 L C {\displaystyle \omega _{\mathrm {res} }={1 \over {\sqrt {LC}}}\,\\!}

Circuit charge  q = q 0 cos ⁡ ( ω t + ϕ ) {\displaystyle q=q_{0}\cos(\omega t+\phi )\,\\!}

Circuit current  I = − ω q 0 sin ⁡ ( ω t + ϕ ) {\displaystyle I=-\omega q_{0}\sin(\omega t+\phi )\,\\!}

Circuit electrical potential energy  U E = q 2 2 C = q 0 2 cos 2 ⁡ ( ω t + ϕ ) 2 C {\displaystyle U_{E}={q^{2} \over 2C}={q_{0}^{2}\cos ^{2}(\omega t+\phi ) \over 2C}\,\\!}

Circuit magnetic potential energy  U B = q 0 2 sin 2 ⁡ ( ω t + ϕ ) 2 C {\displaystyle U_{B}={q_{0}^{2}\sin ^{2}(\omega t+\phi ) \over 2C}\,\\!}

RLC circuits | Circuit equation

L d 2 q d t 2 + R d q d t + q C = E {\displaystyle L{\mathrm {d} ^{2}q \over \mathrm {d} t^{2}}+R{\mathrm {d} q \over \mathrm {d} t}+{q \over C}={\mathcal {E}}\,\\!}

| Circuit equation

L d 2 q d t 2 + R d q d t + q C = E sin ⁡ ( ω 0 t + ϕ ) {\displaystyle L{\mathrm {d} ^{2}q \over \mathrm {d} t^{2}}+R{\mathrm {d} q \over \mathrm {d} t}+{q \over C}={\mathcal {E}}\sin \left(\omega _{0}t+\phi \right)\,\\!}

Circuit charge

q = q 0 e T − R t / 2 L cos ⁡ ( ω ′ t + ϕ ) {\displaystyle q=q_{0}eT^{-Rt/2L}\cos(\omega 't+\phi )\,\\!}

## See also

[edit]

* Defining equation (physical chemistry)
* Fresnel 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

[edit]

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

## Sources

[edit]

* 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 978-81-7758-293-2.

## Further reading

[edit]

* 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 978-0-321-50130-1.

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SI units

Base units|

* ampere
* candela
* kelvin
* kilogram
* metre
* mole
* second

Derived units
with special names|

* becquerel
* coulomb
* degree Celsius
* farad
* gray
* henry
* hertz
* joule
* katal
* lumen
* lux
* newton
* ohm
* pascal
* radian
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* tesla
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Other accepted units|

* astronomical unit
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* day
* decibel
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* minute and second of arc
* neper
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See also|

* Conversion of units
* Metric prefixes
* Historical definitions of the SI base units
* 2019 revision of the SI
* System of units of measurement

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