Which is more ‘fundamental’, the ampere or the coulomb?

©2019 L A Waygood

An American electrical engineer, William J Beaty, who runs the excellent website (challenging the way in which electrical science is taught), entitled ‘K-6 Misconceptions, which I highly recommend, poses the interesting question: ‘Which is the more fundamental: the ampere or the coulomb?’

In his article he argues that, because charge is more fundamental than current, therefore, by extension, the coulomb must be more ‘fundamental’ than the ampere.

As much as admire and agree with most of Mr Beaty’s articles, I feel that in this particular case, he is wrong. I believe that he has made the fundamental mistake of confusing quantities (i.e. ‘current’ and ‘charge’) with their corresponding units of measurement (i.e. ‘ampere’ and ‘coulomb’).

His argument is, essentially, that because electric current is defined in terms of the quantity of charge transferred per unit time, then it follows that the coulomb must, therefore, be more ‘fundamental’ than the ampere.

But SI doesn’t use the term, ‘fundamental’; rather, it uses the term ‘base’. And it considers the ampere to be a ‘base unit‘ while the coulomb is considered to be a ‘derived unit‘. By definition, all ‘derived units’ are defined in terms of ‘base units’.

Where Mr Beaty’s argument falls flat is that he bases most his argument on his belief that the ‘definition’ of the ampere is a ‘coulomb per second’. If this were true, then it would be difficult to disagree with his argument.

But, in fact, the ampere is NOT defined in terms of the coulomb and the second… and it never has been! So, the ampere is not reliant on, and thus ‘less fundamental’ than, the coulomb.

So, if the ampere isn’t defined as a ‘coulomb per second’ (and a lot of North American textbooksm, in particular, mistakenly claim this!), then how is it defined? Well, there are three ‘effects’ of an electric current: the heating effect, the chemical effect, and the magnetic effect. Theoretically, any one of these effects could be used to define its unit of measurement: the ampere. For example, prior to 1948, the ampere was defined in terms of the  chemical effect of an electric current:

The ‘international ampere‘, as it was then called, was an early attempt at defining the ampere, as ‘that current that would deposit 0.001 118 g of silver per second from a silver nitrate solution’

Later, more-accurate measurements revealed that this current was actually 0.999 85 A, and not 1 A as thought! So, in 1948, it was decided to redefine the ampere in terms of the magnetic effect of an electric current! So, since 1948, the ampere has been defined as follows:

The ampere is ‘that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one metre apart in a vacuum, would produce between these conductors a force equal to 2×10−7 newtons per metre of length’.

So, you see, the ampere is not, and never has been, defined as a ‘coulomb per second’! For most of its life, it’s been defined in terms of the force between parallel, current-carrying, conductors.

But, after 70+ years, this definition has now changed! Because, from mid-2019, the ampere is now defined in terms of the rate of flow of elementary charges —i.e. the carried by individual electrons, and NOT by a ‘coulomb’s-worth of electrons’.

This new definition of the ampere us now ‘the current in the direction of flow of a particular number (see elsewhere in this blog for the actual number) of elementary charges per second’.

And, as a ‘derived unit’, SI will continue to define the coulomb in terms of the ampere and the second:

The coulomb is defined as ‘the quantity of charge transferred, in one second, by a steady current of one ampere’.

So, while it is perfectly true that electric charge is ‘more fundamental’ than electric current, the same cannot be said about their corresponding units!

So, to summarise. Mr Beaty is quite correct in arguing that charge is more fundamental than current because current is defined in terms of the quantity of charge transported per unit time.

However, the same argument cannot be extended to the SI unit of current, the ampere, because (contrary to Mr Beaty’s belief) it is an SI base unit, and has never, ever, been defined in terms of the coulomb (a derived unit) but, from 1947, in terms of the force between energised conductors and, since 2019, now in terms of the flow of individual elementary particles.

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