Units in Electricity and Magnetism

The tables below list the systems of electrical and magnetic units.

They only include units of interest in the field of Radio.

The older systems were the CGS(centimeter--) and Gaussian systems.

The Gaussian system being based on a mix of (ESU) and Electromagnetic units (EMU).

The current standard is the International System of Units (SI) and is sometimes referred to as rationalised MKS units.

The MKS system of units is a physical system of units that expresses any given using fundamental units of the , kilogramme, and/or second (MKS)

Conversions from one system to others are given in two ways.

Firstly numerically by multiplying factors.

Note that c stands for the velocity of light in space and its value is exactly 299792458 metre/second exactly (by definition of the metre).

The other method of conversion allows you to change formulas given in old books into the modern SI form. This will be particularly useful to you if, like me, you have books by Terman, Scroggie, etc. or the Admiralty Handbook of Wireless Telegraphy. There were lots of useful formulas in these old books, which can now be given new life.

I have tried to make the tables as complete and accurate as possible and have checked lots of different sources. Nevertheless there may be errors and I will be grateful for any corrections or additions. Please email me at the address given on the home page.

SI Units

Quantity Symbol Unit & (Abbr.) Dimensions ESU EMU

Mass m (kg) M 1000 1000

Length l metre (m) L 100 100

Time t second (s) T 1 1

Power P watt (W) ML2T-3 107 107 I ampere (A) I=M½L1½T-2 10c 0.1

Charge Q (C) TI 10c 0.1

Electric Potential V (V) ML2T-3I-1 106/c 108

Resistance R ( ) ML2T-3I-2 105/c2 109

Conductance G siemens (S) M-1L-2T3I2 10-5c2 10-9

Inductance H henry (H) ML2T-2I-2 105/c2 109

Capacitance C (F) M-1L-2T4I2 10-5c2 10-9

Electric Field Strength E volt/metre (V m-1) MLT-3I-1 104/c 106

Electric Charge Density coulomb/cu.m. (C m-3) L-3TI c/105 10-7

Electric displacement D coulomb/sq.m. (C m-2) L-2TI 4 10-3c 4 10-5 density

Magnetic Potential ampere (A) I 4 10c 4 10-1

Magnetic Field Strength H ampere/metre (A m-1) L-1I 4 c/10 4 10-3

Magnetic flux weber (Wb) ML2T-2I-1 106/c 108

Magnetic Induction B (T) MT-2I-1 100/c 104 Magnetic Flux Density

-4 -2 Magnetic susceptibility e none none 10 c /(4 1/(4 ) )

Magnetic Moment m ampere metre2 (A m2) L2I 105c 103

Magnetisation (Magnetic M ampere/metre (A m-1) L-1I 10-1c 10-3 moment/unit volume)

Magnetic Polarisation J tesla (T) MT-2I-1 102/(4 104/(4 ) c)

Magnetic Pole Strength P ampere metre (A m) LI 103c 10

-1 Magneto Motive Force Fm ampere (A) I 4 10c 4 10

Magnetic Reluctance S ampere/weber(A Wb-1) I2M-1L-2T2 4 10-9 4 10-9

Permittivity of space farad/metre (F m-1) M-1L-3T4I2 - -

Permeability of space henry/metre (H m-1) MLT-2I-2 - - Notes: c (the ) = 299792458 metre/second exactly (by definition of the metre) = 1/(4 10-7c2) = 8.85418781762039 x 10-12 farad/metre (approx) = 4 10-7 = 1.25663706143592 x 10-6 henry/metre (approx)

CGS Units

Quantity Symbol Dimensions Dimensions ESU EMU

Mass m M M gram gram

Length l L L centimetre

Time t T T second second

Power P ML2T-3 ML2T-3 /second erg/second

Electric Current I I M½L1½T-2 statamp biot

Charge Q TI M½L1½T-1 franklin

Electric Potential V ML2T-3I-1 M½L½T-1 (lines/second)

Resistance R ML2T-3I-2 L-1T

Conductance G M-1L-2T3I2 LT-1 statsiemens absiemens

Inductance L ML2T-2I-2 L-1T2 stathenry

Capacitance C M-1L-2T4I2 L cm abfarad

Electric field strength E MLT-3I-1 M½L-½T-1 statvolt/cm abvolt/cm

Electric displacement D L-2TI M½L1½T-1 cm-2 abcoulomb cm- 2

Dielectric constant M-1L-3T4I2 none none none

Magnetic pole P LI M½L2½T-2 unit pole cm-1 = 4 lines of force

Magnetic Potential I M½L1½T-2

Magnetic field strength H L-1I M½L½T-2 Magnetic flux ML2T-2I-1 M½L½

= 1 line

Magnetic Induction B MT-2I-1 M½L-1½ (Magnetic flux density) = 1 line cm-2

Magnetic permeability MLT-2I-2 L-2T2 darcy

Magnetic susceptibility (or k) M½L1½T-2I-1 none none none

Intensity of M (or I) L-1I M½L½T-2 pole cm-2 Magnetisation = J

Magnetic Moment m L2I M½L3½T-2 pole cm

Magneto Motive force G I M½L1½T-2 gilbert

Magnetic Reluctance S L-2M-1T2I2 LT-2 gilbert/biot

Notes: In the first column of Dimensions, I is used as a basic unit. In the second it is expressed in terms of Length, Mass and Time.

Gaussian Units

The Gaussian system uses a mix of Electrostatic and Electromagnetic units There are two common forms, Gaussian and Modified Gaussian, which defines electric current in terms of magnetic units Quantity Symbol Gaussian Modified Gaussian

Electric Current I ESU franklin EMU biot

Charge Q ESU statcoulomb ESU statcoulomb

Electric Potential V ESU statvolt ESU statvolt

Resistance R ESU statohm ESU statohm

Inductance L EMU abhenry cm

Capacitance C cm cm

Electric field strength E ESU statvolt/cm ESU statvolt/cm Electric displacement D ESU statcoulomb/cm2 ESU statcoulomb/cm2

Dielectric constant none none

Magnetic pole P EMU unit pole EMU unit pole

Magnetic Potential EMU gilbert EMU gilbert

Magnetic field strength H EMU oersted EMU oersted

Magnetic flux EMU maxwell EMU maxwell = 1 line = 1 line

Magnetic Induction B EMU gauss EMU gauss (Magnetic flux density)

Magnetic permeability EMU darcy EMU darcy

Magnetic susceptibility none none

Intensity of M EMU pole cm-2 EMU pole cm-2 Magnetisation

Magnetic Moment m EMU pole cm EMU pole cm

Magneto Motive force G EMU gilbert EMU gilbert

Magnetic Reluctance S EMU EMU

Conversion of Gaussian formulae into SI

To convert a formula from the Gauss form into the SI form, replace the elements on both sides of the equation using the table below. Mass, Length, Time and others not listed below are not changed.

Quantity Gaussian SI

Electric Current I I /

Electric Current in EMU I I

Charge Q Q /

Electric Potential, PD, EMF V V

Resistance R R Inductance L L

Capacitance C C / ( )

Electric field strength E E

Electric displacement D D

Dielectric constant /

Magnetic pole P P

Magnetic Potential

Magnetic field strength H H

Magnetic flux

Magnetic Induction B B (Magnetic flux density)

Magnetic permeability /

Magnetic susceptibility or k e

Intensity of Magnetisation I M

Magnetic Moment m m

Magneto Motive force G G

Magnetic Reluctance S S

Example of formula conversion

Maxwell's equations In :

On conversion to SI units these become:

On simplifying

Then using we get:

Approximate ESU/EMU units in terms of SI units

Quantity 1 ESU unit 1 EMU unit Current 334 A 10 A Charge 334 C 10 C Potential 300 V 10 nV Power 100 nW 100 nW Resistance 90 G 1 n Conductance 1 pS 1 GS Inductance 90 GH 1 nH Capacitance 1 pF 1 GF Magnetic flux 300 Wb 10 nWb Magnetic induction 3 MT 100 T Magnetic field strength 3 nA/metre 80 A/metre Magnetisation 33 nA/metre 1000 A/metre Electric field strength 30000 V/metre 1 V/metre Electric displacement 265 nC/metre 8000 C/metre

The electrostatic system of units is a system of units used to measure electrical quantities of , electric current, and within the centimeter-gram-second (or "CGS") system of .

In electrostatic units, electrical charge is defined by the force that it exerts on other charges.

Although the CGS units have mostly been supplanted by the MKSA (meter-kilogram-second- ampere) or International System of Units (SI) units, the electrostatic units are still in occasional use in some applications, most notably in certain fields of physics such as in particle physics and astrophysics.

The main electrostatic units are:

 The statcoulomb, called the franklin or the "esu" for electric charge.

 The statvolt for voltage.

 The gauss for magnetic induction. http://web.archive.org/web/20070129063539/http://www.sciencemuseum.org.uk/on- line/electron/section2/discovery.asp http://www.juliantrubin.com/bigten/millikanoildrop.html