Units in Electricity and Magnetism

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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-gram-second) and Gaussian systems.
The Gaussian system being based on a mix of Electrostatic units (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 measurement using
fundamental units of the metre, 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

kilogram (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

Electric Current

I

ampere (A)

I=M½L1½T-2

10c

0.1

Charge

Q

coulomb (C)

TI

10c

0.1

Electric Potential

V

volt (V)

ML2T-3I-1

106/c

108

Resistance

R

ohm (

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

farad (F)

M-1L-2T4I2

10-5c2

10-9

Electric Field Strength

E

volt/metre (V m-1)

MLT-3I-1

104/c

106

coulomb/cu.m. (C m-3)

L-3TI

c/105

10-7

coulomb/sq.m. (C m-2)

L-2TI

4 10-3c

4 10-5

ampere (A)

I

4 10c

4 10-1

ampere/metre (A m-1)

L-1I

4 c/10

4 10-3

weber (Wb)

ML2T-2I-1

106/c

108

tesla (T)

MT-2I-1

100/c

104

none

none

10-4c-2/(4
)

1/(4 )

Electric Charge Density
Electric displacement
Electric flux density

D

Magnetic Potential
Magnetic Field Strength

H

Magnetic flux
Magnetic Induction
Magnetic Flux Density

B

Magnetic susceptibility

e

)

Magnetic Moment

m

ampere metre2 (A m2)

L2I

105c

103

Magnetisation (Magnetic
moment/unit volume)

M

ampere/metre (A m-1)

L-1I

10-1c

10-3

Magnetic Polarisation

J

tesla (T)

MT-2I-1

102/(4
c)

104/(4 )

Magnetic Pole Strength

P

ampere metre (A m)

LI

103c

10

Magneto Motive Force

Fm

ampere (A)

I

4 10c

4 10-1

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 speed of light) = 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

centimetre

Time

t

T

T

second

second

Power

P

ML2T-3

ML2T-3

erg/second

erg/second

Electric Current

I

I

M½L1½T-2

statamp

biot

Charge

Q

TI

M½L1½T-1

franklin

abcoulomb

Electric Potential

V

ML2T-3I-1

M½L½T-1

statvolt

abvolt
(lines/second)

Resistance

R

ML2T-3I-2

L-1T

statohm

abohm

Conductance

G

M-1L-2T3I2

LT-1

statsiemens

absiemens

Inductance

L

ML2T-2I-2

L-1T2

stathenry

abhenry

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

statcoulomb cm-2

abcoulomb cm2

Dielectric constant
Magnetic pole

P

Magnetic Potential
Magnetic field strength

H

M-1L-3T4I2

none

LI

M½L2½T-2

unit pole
dyne cm-1
= 4 lines of
force

I

M½L1½T-2

gilbert

L-1I

M½L½T-2

oersted

none

none

ML2T-2I-1

Magnetic flux

M½L½

maxwell
= 1 line

Magnetic Induction
(Magnetic flux density)

B

Magnetic permeability
Magnetic susceptibility

(or k)

MT-2I-1

M½L-1½

gauss
= 1 line cm-2

MLT-2I-2

L-2T2

darcy

M½L1½T-2I-1

none

none

none

Intensity of
Magnetisation

M (or I)
=J

L-1I

M½L½T-2

pole cm-2

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

ESU statcoulomb/cm2

ESU statcoulomb/cm2

none

none

EMU unit pole

EMU unit pole

EMU gilbert

EMU gilbert

EMU oersted

EMU oersted

EMU maxwell
= 1 line

EMU maxwell
= 1 line

EMU gauss

EMU gauss

Magnetic permeability

EMU darcy

EMU darcy

Magnetic susceptibility

none

none

Electric displacement

D

Dielectric constant
Magnetic pole

P

Magnetic Potential
Magnetic field strength

H

Magnetic flux
Magnetic Induction
(Magnetic flux density)

B

Intensity of
Magnetisation

M

EMU pole cm-2

EMU pole cm-2

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

Electric Current

I

Electric Current in EMU

I

Charge

Q

Electric Potential, PD, EMF

V

Resistance

R

SI
I/
I
Q/
V
R

Inductance

L

Capacitance

C

Electric field strength

E

Electric displacement

D

L
C/(
E
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

Intensity of Magnetisation

I

Magnetic Moment

m

Magneto Motive force

G

Magnetic Reluctance

S

Example of formula conversion
Maxwell's equations

e

M
m
G
S

In Gaussian units:

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
Charge
Potential
Power
Resistance
Conductance
Inductance
Capacitance
Magnetic flux
Magnetic induction
Magnetic field strength
Magnetisation
Electric field strength
Electric displacement

334 A
334 C
300 V
100 nW
90 G
1 pS
90 GH
1 pF
300 Wb
3 MT
3 nA/metre
33 nA/metre
30000 V/metre
265 nC/metre

10 A
10 C
10 nV
100 nW
1n
1 GS
1 nH
1 GF
10 nWb
100 T
80 A/metre
1000 A/metre
1 V/metre
8000 C/metre

The electrostatic system of units is a system of units used to measure electrical quantities of
electric charge, electric current, and voltage within the centimeter-gram-second (or "CGS")
system of metric units.
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-secondampere) 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/online/electron/section2/discovery.asp
http://www.juliantrubin.com/bigten/millikanoildrop.html

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