How to get a conversion factor in new system of unit

There is some numerical relation $I = \frac{c}{8\pi} E^2$ between the wave intensity $I$ and the electric field strength $E$ written in CGS (centimetre, gram, second) system of units, where $c$ is the speed of light

c = UnitConvert[Quantity["SpeedOfLight"], "Centimeters"/"Seconds"]

where the intensity $I$ is measured in Quantity["Ergs"/"Centimeters"^2/"Seconds"] and the strength $E$ in electrostatic units (ESU) Quantity["ESUsOfElectricField"].

The problem is, firstly, how do I ask Mathematica to obtain the conversion factor in a new system of unit where $I$ is measured in Quantity["Watts"/"Centimeters"^2] and $E$ in Quantity["Volts"/"Centimeters"]

In new system, we should have a relationship like $I = \frac{E^2}{377}$ with the conversion factor $1/377$. How do I get this factor?

Secondly, how can I prove that the dimension of the factor is "Ohms" i.e. $\frac{1}{377\,{\rm Ohms}}$. I could use

UnitConvert[Quantity["ESUsOfElectricField"], "Volts"/"Centimeters"]

149896229/500000 V/cm

or

Solve[Quantity[x1, "ESUsOfElectricField"] ==  Quantity[x2, "Volts"/"Centimeters"], x2]

{{x2 -> (149896229 x1)/500000}}