Statcoulomb: Difference between revisions
imported>Paul Wormer No edit summary |
mNo edit summary |
||
| (4 intermediate revisions by one other user not shown) | |||
| Line 1: | Line 1: | ||
{{subpages}} | {{subpages}} | ||
In [[physics]], a '''statcoulomb''' (symbol '''statC'''), formerly known as '''esu of charge''', is the unit of electric charge in the cgs-esu (centimeter-gram-second electrostatic system) of units. | In [[physics]], a '''statcoulomb''' (symbol '''statC'''), formerly known as '''esu of charge''', is the unit of [[electric charge]] in the cgs-esu (centimeter-gram-second electrostatic system) of units. | ||
By definition, a point charge has magnitude one statcoulomb if it repels a point charge of equal magnitude at a distance of 1 centimeter with a force of one [[dyne]]. | |||
:1 statC = 1 esu of charge = C/(10⋅''c'') ≈ 3.335 640 95⋅10<sup>−10</sup> C | |||
The conversion of statC to C | where C ([[coulomb]]) is the [[SI]] unit of charge and ''c'' is the SI [[speed of light]] (''c'' ≈ 3⋅10<sup>8</sup> m/s). | ||
==Conversion to coulomb== | |||
The conversion of statC to C can be done as follows. Write | |||
: 1 C = ''k'' statC, | : 1 C = ''k'' statC, | ||
and compute ''k''. Consider two charges of 1 C each, 1 m apart, then the force between them is according to [[Coulomb's law]] in SI units, | and compute ''k''. Consider two charges of 1 C each, 1 m apart, then the force between them is according to [[Coulomb's law]] in SI units, | ||
:<math> | :<math> | ||
F = \frac{1}{4\pi \ | F = \frac{1}{4\pi \varepsilon_0} = 10^{-7} c^2\quad \textrm{[N]} | ||
</math> | </math> | ||
(see [[ | (see [[electric constant]] for the SI value of ε<sub>0</sub>). | ||
The same system of two charges has in cgs units a force in dyne (1 dyn = 10<sup>−5</sup> N): | The same system of two charges has in cgs units a force in dyne (1 dyn = 10<sup>−5</sup> N): | ||
:<math> | :<math> | ||
F' = \frac{k^2}{100^2}\; \Longrightarrow\; F' = 10^{-4} k^2\quad\textrm{[dyn]}\;\Longrightarrow\; F = 10^{-9}k^2\quad \textrm{[N]} | F' = \frac{k^2}{100^2}\; \Longrightarrow\; F' = 10^{-4} k^2\quad\textrm{[dyn]}\;\Longrightarrow\; F' = 10^{-9}k^2\quad \textrm{[N]}, | ||
</math> | </math> | ||
Hence | where we applied Coulomb's law in electrostatic units. Hence | ||
:<math> | :<math> | ||
10^{-9}k^2 = 10^{-7} c^2 \;\Longrightarrow\;k = 10 c. | 10^{-9}k^2 = 10^{-7} c^2 \;\Longrightarrow\;k = 10 c. | ||
</math> | </math>[[Category:Suggestion Bot Tag]] | ||
Latest revision as of 06:00, 22 October 2024
In physics, a statcoulomb (symbol statC), formerly known as esu of charge, is the unit of electric charge in the cgs-esu (centimeter-gram-second electrostatic system) of units.
By definition, a point charge has magnitude one statcoulomb if it repels a point charge of equal magnitude at a distance of 1 centimeter with a force of one dyne.
- 1 statC = 1 esu of charge = C/(10⋅c) ≈ 3.335 640 95⋅10−10 C
where C (coulomb) is the SI unit of charge and c is the SI speed of light (c ≈ 3⋅108 m/s).
Conversion to coulomb
The conversion of statC to C can be done as follows. Write
- 1 C = k statC,
and compute k. Consider two charges of 1 C each, 1 m apart, then the force between them is according to Coulomb's law in SI units,
![{\displaystyle F={\frac {1}{4\pi \varepsilon _{0}}}=10^{-7}c^{2}\quad {\textrm {[N]}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6edecd01c713987e8aec3cd43612e3f0176569b2)
(see electric constant for the SI value of ε0). The same system of two charges has in cgs units a force in dyne (1 dyn = 10−5 N):
![{\displaystyle F'={\frac {k^{2}}{100^{2}}}\;\Longrightarrow \;F'=10^{-4}k^{2}\quad {\textrm {[dyn]}}\;\Longrightarrow \;F'=10^{-9}k^{2}\quad {\textrm {[N]}},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9b38178da04ad2cfa7080737339c3604460d946c)
where we applied Coulomb's law in electrostatic units. Hence
