16.2: The CGS Electrostatic System
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Definition. One CGS esu of charge (also known as the statcoulomb) is that charge which, if placed 1 cm from a similar charge in vacuo, will repel it with a force of 1 dyne.
The following exercises will be instructive.
Potential Difference
If the work required to move a charge of 1 esu from one point to another is 1 erg, the potential difference between the points is 1 esu of potential difference, or 1 statvolt.
It is often said that an esu of potential difference is 300 volts, but this is just an approximation. The exact conversion is
1 statvolt=10−8c V.
Capacitance
If the potential difference across the plate of a capacitor is one statvolt when the capacitor holds a charge of one statcoulomb, the capacitance of the capacitor is one centimetre. (No – that's not a misprint.)
1 cm=109c−2F.
Here is a sample of some formulas for use with CGS esu.
Potential at a distance r from a point charge Q in vacuo = Q/r.
Field at a distance r in vacuo from an infinite line charge of λ esu/cm=2λ/r.
Field in vacuo above an infinite charged plate bearing a surface charge density of σ esu/cm2=2πσ.
An electric dipole moment p is, as in SI, the maximum torque experienced by the dipole in unit electric field. A debye is 10−18 esu of dipole moment. The field at a distance r in vacuo along the axis of a dipole is 2p/r.
Gauss's theorem: The total normal outward flux through a closed surface is 4π time the enclosed charge.
Capacitance of a plane parallel capacitor = kA4πd.
Capacitance of an isolated sphere of radius a in vacuo = a. Example: What is the capacitance of a sphere of radius 1 cm? Answer: 1 cm. Easy, eh?
Energy per unit volume or an electric field =E2/(8π).
One more example before leaving esu. You will recall that, if a polarizable material is placed in an electrostatic field, the field D in the material is greater than ϵ0E by the polarization P of the material. That is, D=ϵE+P. The equivalent formula for use with CGS esu is
D=E+4πP
And since P=χeE and D=kE, it follows that
k=1+4πχe.
At this stage you may want a conversion factor between esu and SI for all quantities. I'll supply one a little later, but I want to describe emu first, and then we can construct a table given conversions between all three systems.