Electrostatic Units (ESU) come from Coulomb's Law:
The unit of electric charge in ESU is:
From here we know that .
- Electric Current I:
- Electric Potential ϕ or Voltage V:
- Resistance R:
- Capacitance C:
- Inductance L:
The Electric Field is defined as: [1]
So the unit of electric field in ESU is:
Electromagnetic Units (EMU) come from Ampère's Force Law: [2]
The unit of current here is:
The conversion between Ampere and abA can be derived like (1.1a') and (1.1b'):
By dividing them we get:
We can solve x in : [3]
So we have: [6]
The Magnetic B Field is defined by Lorentz Force: [4]
So the unit of magnetic B field in EMU is:
From (2.1) and (2.2) we get the fact that electric field in ESU and magnetic B field in EMU share the same dimension and unit. This is an advantage of Gaussian Units, where only magnetic quantities (B and H fields, magnetization, vector potential, flux and dipole moment) come from EMU and the others (including inductance L) come from ESU.
There are many equations containing c in Gaussian units, such as Lorentz force:
and Biot-Savart law:
The conversion between tesla and gauss can be derived from:
By dividing them and applying we get:
We can solve x in : [5]
So we have: [6]
The Magnetic Vector Potential A is defined by: [1]
The unit of magnetic vector potential here is G cm or statV, i.e. the same unit as the electric potential ϕ.
From (2.4) we get .
This conversion can also be derived from the definition along with the electric potential ϕ:
By dividing them and applying we get:
We can solve x in : [5]
So we have:
The Magnetic Flux Φ is defined as: [1]
The unit of magnetic flux here is .
From (2.4) we get .
This conversion can also be derived from Faraday's Law of Induction:
By dividing them and applying we get:
We can solve x in : [5]
So we have: [6]
The Magnetic Dipole Moment m is defined by: [1]
where τ is the torque acting on the dipole.
The unit of magnetic dipole moment here is erg/G or statC cm.
From (2.4) we get .
This conversion can also be derived from Amperian loop model:
By dividing them and applying we get:
We can solve x in : [5]
So we have: