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Physics LibreTexts

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=108c 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=109c2F.

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 1018 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.


This page titled 16.2: The CGS Electrostatic System 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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