Gauss Unit System

The Gaussian unit system is a combination of the emu and esu unit subsystems. With three base units, it uses em and es units in magentism and electrostatics, respectively. However, the use of these two subsystems requires the use of the constant \(c\) which is the velocity of light in the vacuum to interrelate these sets of units, resulting in complex and error-prone conversions.
The equivalency betwewn electromagnetic and electrostatic quantities is given in the Table 1, while the equivalence between SI and cgs electromagnetic quantities is shown in Table 2.

Table 1 - The classes of units used for equivalent electromagnetic and electrostatic quantitites.

Electrostatic unts (esu)	Electromagnetic units (emu)
electric charge \(Q\) [Fr]	magentic mass \(m\)
electric current intesity \(I\) \(\left[\frac{\mathrm{Fr}}{\mathrm{s}}\right]\)	magentic flux \(\Phi\) [\(\mathrm{\Gamma}\cdot \mathrm{cm}^2\)]
electric field strength \(\mathrm{E}\)\(\left[\frac{\mathrm{dyne}}{\mathrm{Fr}}\right]\)	magentic field strength \(\mathbf{H}\) \(\left[\frac{\mathrm{Bi}}{\mathrm{cm}}\right]\)
electric displacement \(\mathbf{D}\) \(\left[\frac{\mathrm{Fr}}{\mathrm{cm}^2}\right]\)	induction field \(\mathbf{B}\) \(\left[\frac{\mathrm{dyn}}{\mathrm{Bi\cdot cm}}\right]\)
electirc potential \(V\) \(\left[\frac{\mathrm{erg}}{\mathrm{Fr}}\right]\)	magentic potential \(\mathbf{A}\)
polarization \(\mathbf{P}\)	magentization \(\mathbf{M}\)
electric dipole moment \(\mathbf{p}\) \([\mathrm{Fr}\cdot \mathrm{cm}]\)	magnetic dipole moment m \(\left[\frac{\mathrm{erg}}{\mathrm{\Gamma}}\right]\)
electric susceptibility \(\chi_e\)	magnetic susceptibility \(\chi_m\)
polarizability \(\alpha\)	magentizability \(\xi\)

Table 2 - The equivalence between SI and cgs electric and magnetic quantities.

Physical quantity	SI symbol	cgs (esu and emu) symbol
Electric field strength	\(E\)	\(E\)
Magnetic induction	\(B\)	\(\frac{B}{c}\)
Electric displacement	\(D\)	\(\frac{D}{4\pi}\)
Magnetic field streght	\(H\)	\(\frac{Hc}{4\pi}\)
Dielectric permittivity	\(\varepsilon\)	\(\frac{\varepsilon}{4\pi}\)
Magnetic permeability	\(\mu\)	\(\frac{4\pi\mu}{c^2}\)
Charge density	\(\rho\)	\(\rho\)
Current desnity	\(j\)	\(j\)
Vector potential	\(A\)	\(\frac{A}{c}\)
Hertz vector	\(\pi\)	\(\frac{\pi}{c}\)
Capacitance	\(C\)	\(\frac{C}{4\pi}\)
Inductance	\(L\)	\(\frac{L}{c}\)