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) = μ 0 qm (Am).
Initial quantities
More information Quantity (common name/s), (Common) symbol/s ...
Close
Electric quantities
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
More information , ...
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.
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
J d
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
J c
J
c
=
ρ
v
{\displaystyle \mathbf {J} _{\mathrm {c} }=\rho \mathbf {v} \,\!}
A m−2
[I][L]−2
Close
Electric fields
More information , ...
Quantity (common name/s)
(Common) symbol/s
Defining equation
SI units
Dimension
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
Close
Magnetic quantities
Magnetic transport
More information , ...
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.
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
J m
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)
Close
Magnetic fields
More information , ...
Quantity (common name/s)
(Common) symbol/s
Defining equation
SI units
Dimension
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]
Close
Electric circuits
DC circuits, general definitions
More information , ... Close
AC circuits
More information , ...
Quantity (common name/s)
(Common) symbol/s
Defining equation
SI units
Dimension
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
I 0
I
0
=
I
r
m
s
2
{\displaystyle I_{0}=I_{\mathrm {rms} }{\sqrt {2}}\,\!}
A
[I]
AC root mean square current
I rms
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
V 0
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
V rms
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]
Close
Magnetic circuits
More information , ...
Quantity (common name/s)
(Common) symbol/s
Defining equation
SI units
Dimension
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]
Close