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 :
1
d
y
n
=
(
1
F.
r
)
2
(
1
c
m
)
2
⇔
1
F.
r
=
1
s
t
a
t
C.
=
1
E.
S.
U
=
1
d
y
n
⋅
c
m
{\ 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
This definition is based on Coulomb's law : two equally large charges at a distance repel each other with the force
Q
{\ displaystyle Q}
r
{\ displaystyle r}
F.
=
k
C.
⋅
Q
2
r
2
{\ displaystyle F = k _ {\ mathrm {C}} \ cdot {\ frac {Q ^ {2}} {r ^ {2}}}}
where is Coulomb's constant . In the electrostatic CGS system is dimensionless : .
k
C.
{\ displaystyle k _ {\ mathrm {C}}}
k
C.
=
1
{\ 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
1
F.
r
∼
1
10
m
/
s
c
A.
⋅
s
≈
1
2,997,924,580
C.
≈
3.335
641
⋅
10
-
10
C.
{\ 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
A.
{\ displaystyle \ mathrm {A}}
the coulomb
C.
=
A.
⋅
s
{\ displaystyle \ mathrm {C = A \ cdot s}}
the speed of light .
c
=
299,792,458
m
/
s
{\ displaystyle c = 299,792,458 \ \ mathrm {m / s}}
Electric flow
1
F.
r
∼
1
4th
π
1
10
m
/
s
c
A.
⋅
s
≈
1
37,673,000,000
C.
≈
2.654
4th
⋅
10
-
11
C.
{\ 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
1
F.
r
=
1
d
y
n
⋅
c
m
=
1
G
⋅
c
m
s
⋅
c
m
=
1
⋅
k
G
⋅
m
1000
⋅
100
⋅
s
⋅
m
100
=
1
10
⋅
10,000
⋅
k
G
⋅
m
⋅
m
s
{\ 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
^ Günter Scholz, Klaus Vogelsang: Units, symbols, sizes . Fachbuchverlag Leipzig, 1991, p. 134 .
^ 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).
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