Franklin (unit)

Physical unit
Unit name	Franklin
Unit symbol	${\displaystyle \mathrm {Fr} }$
Physical quantity (s)	Electric charge Electric flow
dimension	${\displaystyle {\mathsf {M^{1/2}\;L^{3/2}\;T^{-1}}}}$
system	Electrostatic CGS unit system , Gaussian CGS unit system
In CGS units	${\displaystyle \mathrm {1\,Fr={\sqrt {dyn}}\cdot cm=1\;{\frac {\sqrt {g\cdot cm^{3}}}{s}}} }$
Named after	Benjamin Franklin

The Franklin ( unit symbol  Fr , after the American naturalist and inventor Benjamin Franklin ; synonymous name: Statcoulomb or statC ) is the unit for electrical charge and electrical flow in the cgs-based electrostatic unit system  (ESU) and in the Gaussian system of units .

In the European Union and Switzerland, the Franklin is not a legal entity .

definition

The Franklin is defined as follows: For two bodies 1 cm apart, both of which carry the charge 1 Franklin, the repulsive force is 1  dyn :

${\displaystyle {\begin{aligned}1\ \mathrm {dyn} &=\mathrm {\frac {(1\ Fr)^{2}}{(1\ cm)^{2}}} \\\Leftrightarrow 1\ \mathrm {Fr=1\,statC=1\,ESU} &=1\ \mathrm {{\sqrt {dyn}}\cdot cm} \end{aligned}}}$

With

• ${\displaystyle \mathrm {ESU} }$as a placeholder for the electrical charge .

This definition is based on Coulomb's law : two equally large charges at a distance repel each other with the force ${\displaystyle Q}$ ${\displaystyle r}$

${\displaystyle F=k_{\mathrm {C} }\cdot {\frac {Q^{2}}{r^{2}}}}$

where is Coulomb's constant . In the electrostatic CGS system is dimensionless : . ${\displaystyle k_{\mathrm {C} }}$ ${\displaystyle k_{\mathrm {C} }=1}$

conversion

Corresponding SI unit

Units from different systems of units may not officially be used together; so the Franklin or the units derived from it may not be used in equations together with the corresponding SI unit Coulomb .

The factor for converting to coulombs depends on which size is to be given in Franklin.

Electric charge

${\displaystyle {\begin{aligned}1\ \mathrm {Fr} &\sim {\frac {1}{10}}\ {\frac {\mathrm {m/s} }{c}}\ \mathrm {A\cdot s} \\&\approx {\frac {1}{2.997.924.580}}\ \mathrm {C} \\&\approx 3{,}335641\cdot 10^{-10}\ \mathrm {C} \end{aligned}}}$

With

• the amp ${\displaystyle \mathrm {A} }$
• the coulomb ${\displaystyle \mathrm {C=A\cdot s} }$
• the speed of light . ${\displaystyle c=299.792.458\ \mathrm {m/s} }$

Electric flow

${\displaystyle {\begin{aligned}1\ \mathrm {Fr} &\sim {\frac {1}{4\ \pi }}\ {\frac {1}{10}}\ {\frac {\mathrm {m/s} }{c}}\ \mathrm {A\cdot s} \\&\approx {\frac {1}{37.673.000.000}}\ \mathrm {C} \\&\approx 2{,}6544\cdot 10^{-11}\ \mathrm {C} \end{aligned}}}$

CGS base units

${\displaystyle {\begin{aligned}1\ \mathrm {Fr} &=\mathrm {1\ {\sqrt {dyn}}\cdot cm} \\&=\mathrm {1\ {\frac {\sqrt {g\cdot cm}}{s}}\cdot cm} \\&=\mathrm {{\frac {1\cdot {\sqrt {kg\cdot m}}}{{\sqrt {1000\cdot 100}}\cdot s}}\cdot {\frac {m}{100}}} \\&=\mathrm {{\frac {1}{{\sqrt {10}}\cdot 10.000}}\cdot {\frac {{\sqrt {kg\cdot m}}\cdot m}{s}}} \end{aligned}}}$

Individual evidence

1. ^ Günter Scholz, Klaus Vogelsang: Units, symbols, sizes . Fachbuchverlag Leipzig, 1991, p. 134 .
2. ^ Ari L Horvath: Conversion Tables of Units in Science & Engineering . Springer, 1986, ISBN 1-349-08559-6 , pp. 113 ( limited preview in Google Book search).