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Physics LibreTexts

16.5: Conversion Factors

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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 4π 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 58×1010, which is numerically equal to the speed of light expressed in cm s1. 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 = 101c statcoulomb = 101 emu

Electric Current

1 amp = 101c esu = 101 abamp

Potential Difference

1 volt = 108/c statvolt = 108 emu

Resistance

1 ohm = 109/c2 esu = 109 abohm

Capacitance

1 farad = 109c2 esu = 109 emu

Inductance

1 henry = 109/c2 esu = 109 emu

Electric Field E

1 V m1 = 106/c esu = 106 esu

Electric Field D

1 C m2 = 4π×105c esu = 4π×105 emu

Magnetic Field B

1 tesla = 104/c esu = 104 gauss

Magnetic Field H

1 A m1 = 4π×103c esu = 4π×103 oersted

Magnetic B-flux FB

1 weber = 108/c esu = 108 maxwell


This page titled 16.5: Conversion Factors is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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