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This has to do with the SI definition of the Ampere. Why the quantity $2*10^{-7} $ Newtons in particular? It would make more sense to define 1 Ampere = 1 mole of electron charge per second. Which would be equivalent to 1 Farad/second. The Ampere is not a static unit since it is based on moving electrons. But is there a history as to why they chose that particular amount of force between 2 infinitely long wires 1 meter apart?

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  • $\begingroup$ Maybe because it's hard to realize one mole electrons, but that's only a wild guess and I'm looking forward for an answer. $\endgroup$ – Jasper Jan 29 '19 at 17:23
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    $\begingroup$ The number of electrons to make 1 C is not Avagodro's number. $\endgroup$ – The Photon Jan 29 '19 at 17:29
  • $\begingroup$ Also, FWIW, the ampere was defined with essentially its current value in 1893, but the charge on the electron wasn't measured until 1909. $\endgroup$ – The Photon Jan 29 '19 at 17:38
  • $\begingroup$ 1 mole of electrons per second is an enormous electrical current, equal to 96320 amps, as the amp is currently defined! And note - 1 mole of electrons per second is NOT equal to 1 Farad per second - you are mixing your units. $\endgroup$ – David White Jan 30 '19 at 1:05
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Modern SI unit definitions link the value of a unit to a particular mechanical measurement, so that the various base units can be calibrated independently of each other. This is why the definition of the ampere is in terms of an actual mechanical experiment involving two current-carrying wires, long enough that the finite-size corrections don't matter for the precision you want (which is what "infinite" means in practice).

This definition came from an equivalent, easier-to-understand definition of the ampere as "1 coulomb of charge per second." A current of 1 coulomb per second in two wires 1 meter apart will give you a force of $2\times 10^{-7}$ Newtons. The coulomb is not an SI base unit; fully expanded in SI base units, 1 coulomb is 1 ampere-second. Defining the coulomb in terms of the ampere, instead of the other way around, is a choice that is made out of convenience; nowadays, it's far easier to get a steady 1-ampere current in an experimental setting than it is to retain a steady charge of 1 coulomb. Because of this, it's much easier to describe the base electromagnetic unit in terms of a force measurement (which we can do very precisely and easily) rather than a charge measurement (which is harder).

Also, for the record, 1 mole of electrons gives you a charge of $6.022\times 10^{23}*1.6\times 10^{-19}\;\mathrm{C}=96352\;\mathrm{C}$, which, if passed through a wire in one second, would give you a current of $96352$ amperes. The number of electrons that you're looking for is $\frac{1}{1.6\times 10^{-19}}=6.25\times 10^{18}$ electrons, or $1.03\times 10^{-5}$ moles of electrons. The farad, being a unit of capacitance, is irrelevant here.

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  • $\begingroup$ Which then leads me to ask, where did the original Coulomb unit come from? $\endgroup$ – Mr X Jan 29 '19 at 18:42
  • $\begingroup$ 1 Farad = the amount of charge in 1 mole of electrons. Which is why I mentioned it. $\endgroup$ – Mr X Jan 29 '19 at 18:47
  • $\begingroup$ @Mr X: Its one Faraday that is a mole of electrons, not a Farad which is unit of capacitance. $\endgroup$ – mike stone Jan 29 '19 at 20:45
  • $\begingroup$ @mikestone I hadn't actually heard of that unit before. This makes the question make a bit more sense. $\endgroup$ – probably_someone Jan 29 '19 at 22:19
  • $\begingroup$ @MrX As far as I can tell, the SI coulomb was always defined as "the amount of charge accumulated due to 1 ampere of current in 1 second," going back to the 1881 International Electrical Congress at which it was defined (and whose definitions the SI later adopted). $\endgroup$ – probably_someone Jan 29 '19 at 22:26
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The SI system has just be revised so that the electron charge is exactly $$ e= 1.602176634 \times 10^{-19} {\rm C} $$ and a current of one ampere is 1 C per second. Thus the $2\times 10^{-7}$ definition is obsolete and the new definition is along the lines you suggest. Similarly a mole is now exactly $6.02214076\times 10^{23}$ elementary entities.

Here is text from Wkipedia. It agrees with what I read in the physics literature:

"A consequence of this change is that the new definition of the kilogram is dependent on the definitions of the second and the metre.

Ampere: The definition of the ampere underwent a major revision – the previous definition, which is difficult to realise with high precision in practice, was replaced by a definition that is more intuitive and easier to realise.

Previous definition: The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2$\times 10^{-7}$ newton per metre of length.

2019 definition: The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge $e$ to be 1.602176634 $\times 10^{−19}$ when expressed in the unit C, which is equal to A⋅s, where the second is defined in terms of $\Delta \nu \,{\rm C}\cdot {\rm s}$."

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