16.5: Conversion Factors

Last updated
Save as PDF

Page ID: 5519

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

By this time, you are completely bewildered, and you want nothing to do with such a system. Indeed you may even be wondering if I made it all up, so irrational does it appear to be. You would like to ignore it all completely. But you cannot ignore it, because, in your reading, you keep coming across formulas that you need, but you don’t know what units to use, or whether there should be a \(4 \pi\) in the formula, or whether there is a permittivity or permeability missing from the equation because the author happens to be using some set of units in which one or the other of these quantities has the numerical value 1, or whether the \(H\) in the equation should really be a \(B\), or the \(E\) a \(D\).

Is there anything I can do to help?

What I am going to do in this section is to list a number of conversion factors between the different systems of units. This may help a little, but it won’t by any means completely solve the problem. Really to try and sort out what a CGS equation means requires some dimensional analysis, and I shall address that in section 16.6

In the conversion factors that I list in this section, the symbol c stands for the number \(2.997 \ 924 \ 58 \times 10^{10}\), which is numerically equal to the speed of light expressed in \(\text{cm s}^{-1}\). The abbreviation “esu” will mean CGS electrostatic unit, and “emu” will mean CGS electromagnetic unit. A prefix “stat” to a unit implies that it is an esu; a prefix “ab” implies that it is an emu. I list the conversion factors for each quantity in the form “1 SI unit = so many esu = so many emu”.

I might mention that people will say that “SI is full of conversion factors”. The fact is that SI is a unified coherent set of units, and it has no conversion factors. Conversion factors are characteristic of CGS electricity and magnetism.

Quantity of Electricity (Electric Charge)

1 coulomb = \(10^{-1} c \) statcoulomb = \(10^{-1}\) emu

Electric Current

1 amp = \(10^{-1} c\) esu = \(10^{-1}\) abamp

Potential Difference

1 volt = \(10^8/c\) statvolt = \(10^8\) emu

Resistance

1 ohm = \(10^9/c^2\) esu = \(10^9\) abohm

Capacitance

1 farad = \(10^{-9}c^2\) esu = \(10^{-9}\) emu

Inductance

1 henry = \(10^9/c^2\) esu = \(10^9\) emu

Electric Field E

1 \(\text{V m}^{-1}\) = \(10^6/c\) esu = \(10^6\) esu

Electric Field D

1 \(\text{C m}^{-2}\) = \(4 \pi \times 10^{-5}c\) esu = \(4 \pi \times 10^{-5}\) emu

Magnetic Field B

1 tesla = \(10^4/c\) esu = \(10^4\) gauss

Magnetic Field H

1 \(\text{A m}^{-1}\) = \(4 \pi \times 10^{-3}c\) esu = \(4 \pi \times 10^{-3}\) oersted

Magnetic B-flux F_B

1 weber = \(10^8/c\) esu = \(10^8\) maxwell