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electric units

 Definition/Summary Electric and magnetic units have symbols which are (or begin with) a capital letter, but have names which begin with a small letter. The units below (except for eV) are SI units. dim. = dimension; M = mass; L = length; T = time; Q = charge. Units such as $A.s^{-1}$ have been written as fractions, to make easier comparison between different units, but this is generally bad practice, and is not to be copied.

 Equations Charge (dim. $Q$): $$\text{C}\ \equiv\ \text{coulomb}$$ Current = charge/time = energy/magnetic flux (dim. $Q/T$): $$\text{A}\ \equiv\ \text{amp (or ampere)}\ \equiv\ \frac{\text{C}}{\text{s}}\ \equiv\ \frac{\text{coulomb}}{\text{second}}\ \equiv\ \frac{\text{J}}{\text{Wb}}\ \equiv\ \frac{\text{joule}}{\text{weber}}$$ Magnetic flux = voltage.time = energy/current (dim. $ML^2/QT$): $$\text{Wb}\ \equiv\ \text{weber}\ \equiv\ \text{V.s}\ \equiv\ \text{volt.second}\ \equiv\ \frac{\text{J.s}}{\text{C}}\ \equiv\ \frac{\text{joule.second}}{\text{coulomb}}$$ Magnetic pole-strength: $$\text{A-m}\ \equiv\ \text{amp-metre}$$ Magnetic dipole moment = pole-strength.distance = current.area: $$\text{A-m.m}\ \equiv\ \text{A.m}^2\ \equiv\ \text{amp-square metre}\ \equiv\ \frac{\text{J}}{\text{T}}\ \equiv\ \frac{\text{joule}}{\text{tesla}}$$ Magnetic intensity ($\boldsymbol{H}$) and magnetisation density ($\boldsymbol{M}$) = current/distance (dim. $Q/LT$): $$\frac{\text{A}}{\text{m}}\ \equiv\ \frac{\text{amp-turns}}{\text{metre}}\ \equiv\ \frac{\text{amp}}{\text{metre}}\ \equiv\ \frac{\text{A-m.m}}{\text{m}^3}\ \equiv\ \frac{\text{magnetic dipole moment}}{\text{volume}}$$ Electric potential = voltage = energy/charge = emf (dim. $ML^2/QT^2$): $$\text{V}\ \equiv\ \text{volt}\ \equiv\ \frac{\text{J}}{\text{C}}\ \equiv\ \frac{\text{joule}}{\text{coulomb}}\ \equiv\ \frac{\text{W.s}}{\text{C}}\ \equiv\ \frac{\text{watt.second}}{\text{coulomb}}\ \equiv\ \frac{\text{W}}{\text{A}}\ \equiv\ \frac{\text{watt}}{\text{amp}}$$ Power = voltage.current = energy/time (dim. $ML^2/T^3$): $$\text{W}\ \equiv\ \text{watt}\ \equiv\ \frac{\text{J}}{\text{s}}\ \equiv\ \frac{\text{joule}}{\text{second}}\ \equiv\ \frac{\text{N.m}}{\text{s}}\ \equiv\ \frac{\text{newton.metre}}{\text{second}}\ \equiv\ \text{V.A}\ \equiv\ \text{volt.amp}\ \equiv\ \Omega\text{.A}^2\ \equiv\ \text{ohm.amp}^2$$ Energy = voltage.charge (dim. $ML^2/T^2$): $$\text{J}\ \equiv\ \text{joule}\ \equiv\ \text{CV}\ \equiv\ \text{coulomb.volt}\ \equiv\ \frac{\text{eV}}{1.602\ 10^{-19}}\ \equiv\ \frac{\text{electron.volt}}{1.602\ 10^{-19}}$$ Energy density = energy/volume = work done/volume = force/area = pressure (dim. $M/LT^2$): $$\text{Pa}\ \equiv\ \text{pascal}\ \equiv\ \frac{\text{J}}{\text{m}^3}\ \equiv\ \frac{\text{joule}}{\text{metre}^3}\ \equiv\ \frac{\text{N}}{\text{m}^2}\ \equiv\ \frac{\text{N}}{\text{C}}\ \frac{\text{C}}{\text{m}^2}\ \equiv\ \frac{\text{N}}{\text{A.m}}\ \frac{\text{A}}{\text{m}}\ \equiv\ \frac{\text{newton}}{\text{metre}^2}$$ Impedance ($Z\ =\ R\ +\ jX$) (resistance plus $j$reactance) = voltage/current = electric field per magnetic intensity ($\boldsymbol{E}/\boldsymbol{H}$) = power/current-squared = inductance/time = inductance.frequency (dim. $ML^2/Q^2T$): $$\Omega\ \equiv\ \text{ohm}\ \equiv\ \frac{\text{V}}{\text{A}}\ \equiv\ \frac{\text{volt}}{\text{amp}}\ \equiv\ \frac{\text{W}}{\text {A}^2}\ \equiv\ \frac{\text{watt}}{\text{amp}^2}\ \equiv\ \frac{\text{H}}{\text {s}}\ \equiv\ \frac{\text{henry}}{\text{second}}$$ Conductance = current/voltage = capacitance/time = capacitance.frequency (dim. $Q^2T/ML^2$): $$S\text{ or }\mho\ \equiv\ \text{siemens}\ \equiv\ \frac{\text{A}}{\text{V}}\ \equiv\ \frac{\text{amp}}{\text{volt}}\ \equiv\ \frac{\text{F}}{\text {s}}\ \equiv\ \frac{\text{farad}}{\text{second}}$$ Inductance = magnetic flux/current = voltage.time/current = energy.time-squared/charge-squared (dim. $ML^2/Q^2$): $$\begin{eqnarray*} \text{H} & \equiv & \text{henry}\ \equiv\ \frac{\text{Wb}}{\text{A}}\ \equiv\ \frac{\text{weber}}{\text{amp}}\ \equiv\ \frac{\text{V.s}}{\text{A}}\ \equiv\ \frac{\text{volt.second}}{\text{amp}}\ \equiv\ \Omega\text{.s}\ \equiv\ \text{ohm.second}\\ & \equiv & \frac{\text{J.s}^2}{\text{C}^2}\ \equiv\ \frac{\text{joule.second}^{\,2}}{\text{coulomb}^{\,2}}\ \equiv\ \frac{\text{s}^2}{\text{F}}\ \equiv\ \frac{\text{second}^{\,2}}{\text{farad}} \end{eqnarray*}$$ Capacitance = charge/voltage = current.time/voltage = charge-squared/energy (dim. $Q^2T^2/ML^2$): $$\begin{eqnarray*} \text{F} & \equiv & \text{farad}\ \equiv\ \frac{\text{C}}{\text{V}}\ \equiv\ \frac{\text{coulomb}}{\text{volt}}\ \equiv\ \frac{\text{C}^2}{\text{J}}\ \equiv\ \frac{\text{coulomb}^{\,2}}{\text{joule}}\ \equiv\ \frac{\text{C}^{\,2}}{\text{N.m}}\ \equiv\ \frac{\text{coulomb}^2}{\text{newton.metre}}\\ & \equiv & \frac{\text{A.s}}{\text{V}}\ \equiv\ \frac{\text{amp.second}}{\text{volt}}\ \equiv\ \frac{\text{s}}{\Omega}\ \equiv\ \frac{\text{second}}{\text{ohm}} \end{eqnarray*}$$ Electric field ($\boldsymbol{E}$) = force/charge = voltage/distance (dim. $ML/QT^2$): $$\frac{\text{N}}{\text{C}}\ \equiv\ \frac{\text{newton}}{\text{coulomb}} \equiv\ \frac{\text{V}}{\text{m}}\ \equiv\ \frac{\text{volt}}{\text{metre}}$$ Electric displacement field ($\boldsymbol{D}$) and polarisation density ($\boldsymbol{P}$) = charge/area (dim. $Q/L^2$): $$\frac{\text{C}}{\text{m}^2}\ \equiv\ \frac{\text{coulomb}}{\text{metre}^2}$$ Magnetic field ($\boldsymbol{B}$) = force/charge.speed = magnetic flux/area = voltage.time/area = force/current.distance = mass/charge.time = mass/current.time-squared = energy.time/charge.area (dim. $M/QT$): $$\begin{eqnarray*} \text{T} & \equiv & \text{tesla}\ \equiv\ \frac{\text{Wb}}{\text{m}^2}\ \equiv\ \frac{\text{weber}}{\text{metre}^2}\ \equiv\ \frac{\text{V.s}}{\text{m}^2}\ \equiv\ \frac{\text{volt.second}}{\text{metre}^2}\\ & \equiv & \frac{\text{N}}{\text{A.m}}\ \equiv\ \frac{\text{newton}}{\text{amp.metre}}\ \equiv\ \frac{\text{kg}}{\text{C.s}}\ \equiv\ \frac{\text{kilogram}}{\text{coulomb.second}}\ \equiv\ \frac{\text{kg}}{\text{A.s}^2}\ \equiv\ \frac{\text{kilogram}}{\text{amp.second}^{\,2}} \end{eqnarray*}$$ Time (dim. $T$): $$\text{s}\ \equiv\ \text{second}\ \equiv\ \frac{\text{H}}{\Omega}\ \equiv\ \frac{\text{henry}}{\text{ohm}}\ \equiv\ \Omega\text{.F}\ \equiv\ \text{ohm.farad}\ \equiv\ \text{H}^{1/2}\text{.F}^{1/2}\ \equiv\ \text{henry}^{1/2}\text{.farad}^{1/2}$$

 Recent forum threads on electric units

 Breakdown Physics > Electromagnetism >> Physical Quantities & Units

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 Extended explanation Two ways of defining voltage: voltage = energy/charge = work/charge = force"dot"distance/charge = (from the Lorentz force) electric field"dot"distance, or dV = E.dr but also voltage = energy/charge = (energy/time)/(charge/time) = power/current, or V = W/I Velocity: Note that, dimensionally, the relationship between the electric and magnetic fields $\mathbf{E}$ and $\mathbf{B}$ is the inverse of the analogous relationship between $\mathbf{D}$ and $\mathbf{H}$ or between $\mathbf{P}$ and $\mathbf{M}$: $$\text{velocity}\ =\ \frac{\text{electric field (E)}}{magnetic\text{ field (B)}}\ =\ \frac{magnetic\text{ intensity (H)}}{\text{electric displacement field (D)}}\ =\ \frac{magnetic\text{ density (M)}}{\text{polarisation density (P)}}$$ and so, for example, we expect to find $(1/c)\mathbf{E}$ and $\mathbf{B}$ together, but $c\mathbf{D}$ and $\mathbf{H}$ together, and $c\mathbf{P}$ and $\mathbf{M}$ together. Time constants: In "RLC" AC circuits (with resistance R, inductance L and/or capacitance C), combinations with dimensions of time, such as RC, or L/R, occur as "time constants", and combinations with dimensions of 1/time, such as $\sqrt{(1/LC - R^2/4L^2)}$, occur as frequencies. Electric displacement field: The electric displacement field was designed specifically for parallel-plate capacitors: it is always $Q/A$, the charge (on either plate) divided by the area, in coulombs per square metre ($C/m^2$). Permittivity and permeability: Permittivity (a tensor) = capacitance/distance = electric displacement field/electric field (dim. $Q^2T^2/ML^3$): $$\frac{\text{F}}{\text{m}}\ =\ \frac{\text{farad}}{\text{metre}}$$ $$\mathbf{D}\ =\ \widetilde{\mathbf{\varepsilon}}\mathbf{E}\ =\ \varepsilon_0\,\mathbf{E}\ +\ \mathbf{P}\ \,\text{(or }\mathbf{E}\ =\ \mu_0\,c^2\,(\mathbf{D}\ -\ \mathbf{P})\ \text{)}$$ Permeability (a tensor) = inductance/distance = magnetic field/auxiliary magnetic field (dim. $ML/Q^2$): $$\frac{\text{H}}{\text{m}}\ =\ \frac{\text{henry}}{\text{metre}}\ =\ \frac{\text{T.m}}{\text{A}}\ =\ \frac{\text{tesla.metre}}{\text{amp}}\ =\ \frac{\text{N}}{\text{A}^2}\ =\ \frac{\text{newton}}{\text{amp}^2}$$ $$\mathbf{H} = \widetilde{\mathbf{\mu}}^{-1}\mathbf{B}\ =\ \frac{1}{\mu_0}\,\mathbf{B}\ \,-\ \,\mathbf{M}\ \,\text{(or }\mathbf{B}\ =\ \mu_0(\mathbf{H}\ +\ \mathbf{M})\ \text{)}$$ Note that, since the magnetic analogies of ${\mathbf{E}}$ and ${\mathbf{D}}$ are ${\mathbf{B}}$ and ${\mathbf{H}}$, respectively, the magnetic analogy of permittivity is the inverse of permeability, and the magnetic analogy of $\mathbf{P}$ is minus $\mathbf{M}$. This is purely for historical reasons. Permeability times permittivity = 1/velocity-squared (dim. $T^2/L^2$): $$\widetilde{\mathbf{\varepsilon}}\widetilde{\mathbf{\mu}}\ =\ \frac{1}{v^2}$$ Vacuum constants: Vacuum permeability is defined as exactly: $$\mu_0\ \equiv\ 4\pi\,10^{-7}\ \text{H/m}$$ which is approximately: $1.26\,10^{-6}\ \text{H/m}$ Vacuum permittivity is defined as exactly: $$\varepsilon_0\ \equiv\ \frac{1}{\mu_0\,c^2}$$ which is approximately: $8.85 \, 10^{-12}\ \text{F/m}$ (If it wasn't for that arbitrary $10^{-7}$ in the definition of $\mu_0$, then $\varepsilon_0$ would simply be $1/4\pi c^2 F/m$)Characteristic impedance of vacuum ($Z_0=\mu_0c$) is defined as exactly: $$Z_0\ =\ 119.9169832\pi\ \Omega$$ which is approximately: $376.73\ \Omega$ cgs units: The following are cgs units, and more details may be found at http://en.wikipedia.org/wiki/CGS and http://www.qsl.net/g4cnn/units/units.htm: esu (charge) biot (current) statvolt (electric potential) maxwell (magnetic flux) oersted (magnetic intensity, $\mathbf{H}$) gauss (magnetic field, $\mathbf{B}$)

Commentary

 tiny-tim @ 03:08 AM Dec9-12 Added energy density, and http://www.qsl.net/g4cnn/units/units.htm

 tiny-tim @ 03:58 PM Apr2-12 Added "amp-turns", "H = Ω.s", "F = s/Ω".

 tiny-tim @ 05:42 PM Feb23-12 Added magnetic pole-strength and magnetic dipole moment.

 tiny-tim @ 06:31 AM Apr1-11 Minor changes to permittivity and vacuum permittivity

 tiny-tim @ 05:25 PM Mar14-11 Added H = s²/F and time constants.

 tiny-tim @ 05:33 AM Jun9-10 corrected 1019 to 10-19 (in electron volts)

 tiny-tim @ 04:03 AM Dec28-09 Added impedance, E/H, H/s, and F/s. Removed repetition of current. Changed the order of some items. Added characteristic impedance of vacuum.

 tiny-tim @ 09:50 AM Mar28-09 Added siemens (conductance)

 tiny-tim @ 03:42 PM Mar1-09 Added "Two ways of defining voltage"

 tiny-tim @ 05:16 PM Sep28-08 clicked "edit" and "save" without changing anything, so as to restore the LaTeX.

 tiny-tim @ 09:03 AM Aug4-08 Added that the magnetic analogy of permittivity is the inverse of permeability. Added polarisation density (P) and magnetisation density (M), and comment on velocity.

 tiny-tim @ 11:11 AM Jul29-08 Amended Extended explanation. Had got permeability and permittivity the wrong way round (why did nobody spot that?). Added tesla.metre/amp. Added vaccuum constants.

 tiny-tim @ 01:01 PM Jul16-08 Added electric displacement field (D).