# Electrostatic system of units

The electrostatic unit system (in short ESU for e lectro s tatic u nits , German esu electrostatic units) is a physical unit system , which on the CGS system builds up and this order electromagnetic supplemented units.

## definition

The electrostatic system of units is based on the greatest possible simplification of Coulomb's law of electrostatics , which determines the force between two electrical charges and depending on their distance : ${\ displaystyle F}$ ${\ displaystyle q_ {1}}$${\ displaystyle q_ {2}}$${\ displaystyle r}$

${\ displaystyle F = k _ {\ mathrm {C}} {\ frac {q_ {1} q_ {2}} {r ^ {2}}}}$

The Coulomb's constant is equal to one in the electrostatic unit system, while electromagnetic units (EMU) the value in CGS system and in the SI system the value has. Here is the speed of light in a vacuum and the electric field constant . ${\ displaystyle k _ {\ mathrm {C}}}$${\ displaystyle k _ {\ mathrm {C}} = 1 / c ^ {2}}$${\ displaystyle k _ {\ mathrm {C}} = 1 / (4 \ pi \ varepsilon _ {0})}$${\ displaystyle c}$${\ displaystyle \ varepsilon _ {0}}$

The unit of force in the electrostatic unit system is the CGS unit dyne = 1 g · cm / s ², the distance between the charges is in cm measured. The charge has the same unit in the electrostatic system of units

${\ displaystyle [q] = {\ sqrt {\ mathrm {dyn}}} \ cdot \ mathrm {cm} = {\ sqrt {\ mathrm {g} \ cdot \ mathrm {cm} ^ {3}}} \ cdot \ mathrm {s} ^ {- 1} =: \ mathrm {statC}}$

The so defined unit statC is also used in the Gaussian system of units and bears the name Franklin (Fr).

## [esu] as a placeholder

In invoices in the cgs system, the abbreviation [esu] is used as a placeholder for a specific unit. Here is esu often enclosed in square brackets, not to be confused with a concrete unit.

For example

• for the electrical capacity : ${\ displaystyle 1 ~ [{\ rm {esu}}] = 1 ~ {\ rm {cm}}}$
• for the electric charge :${\ displaystyle 1 ~ [{\ rm {esu}}] = 1 ~ {\ sqrt {\ rm {dyn}}} ~ {\ rm {cm}} = 1 ~ {\ rm {statC}}}$
• for the electrical current : ${\ displaystyle 1 ~ [{\ rm {esu}}] = 1 ~ {\ sqrt {\ rm {dyn}}} ~ {\ rm {cm / s}} = 1 ~ {\ rm {statA}}}$

A current of one statA corresponds to a current of amperes in SI units. ${\ displaystyle 10 / c}$