Converting Electromagnetic Units: Gaussian to Superfluous Systems

[gerald V]

Recently, I tried to convert an energy density $\frac{gram}{cm^3}$ into $(\frac{Volt}{cm})^2$. I faced some problems originating from the introduction of the superfluous unit $Ampere$ and its descendants in the system of units.

On one hand, there are the transparent Gaussian units, in particular $1 Franklin \equiv 1 statCoulomb = 1 \sqrt{\frac{gram \cdot cm^3}{sec^2}}$ and $1 statVolt \equiv 1 \frac{erg}{StatCoulomb} = 1 \sqrt{\frac{gram \cdot cm}{sec^2}}$.

The conversion to the superfluous units involves a dimensionful factor, namely the velocity of light. I found somewhere on the web (I cannot not find this page again) $1 Volt = \frac{10^8}{c}StatVolt = 1 \frac{sec}{298 \cdot cm} StatVolt = \frac{1}{298} \sqrt{\frac{gram}{cm}}$, and this straightforwardly allows the conversion of the energy density units.

However, on a number of Wikipedia pages, this dimensionful factor is missing and only the numerical value of the velocity of light in our usual units appears (https://en.wikipedia.org/wiki/Statvolt). The same holds for the $Coulomb$, where the German page is the more detailed one (see section "Historisches" of https://de.wikipedia.org/wiki/Coulomb). In the relation between $Coulomb$ and $Franklin$, in my opinion the dimensionful denominator $\frac{1 \; meter}{sec}$ is to be removed (whether the numerical factors are correct then, I do not know). Am I right?

I am aware that there are even more units around, in particular electrostatic vs. electrodynamic, which sounds after the involvement of the velocity of light. However, does this affect the units discussed above?

Thank you in advance for any answer.

 

[Dale]

To me it is not clear that there is a unique correct conversion factor. Maxwell’s equations are different in the different unit systems, so the correct conversion may depend on the context. Are you comparing a Gaussian unit in a Gaussian formula with the SI equivalent unit in the SI equivalent formula, or are you using a SI formula and comparing the native SI quantity with the equivalent Gaussian formula, or similarly with a Gaussian formula. It may even depend on which formula is being used.

 

[gerald V]

Thank you very much. Meanwhile I realized that I made an ultimately ridiculous error. The energy density has dimension $\frac{gram}{cm \cdot sec^2}$ rather than $\frac{gram}{cm^3}$. With this, everything is clear. Being so used to setting the velocity of light unity, I managed to forget the one and only physical formula the entire world knows. Sorry.