Which is more ‘fundamental’, Current or Charge?

©2019 L A Waygood

An American electrical engineer, William J Beaty, who runs the excellent website, ‘K-6 Misconceptions, which I highly recommend, poses the interesting question: ‘Which is the more fundamental: Current or Charge?’

In his article, he argues that charge is more fundamental than current and, 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 has gone astray. I believe that he has made the fundamental mistake of confusing quantities (i.e. ‘current’ and ‘charge’) and 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.

SI doesn’t use the term, ‘fundamental’. But it does consider the ampere to be a ‘base unit‘ and the coulomb to be a ‘derived unit‘.

Where Mr Beaty’s argument fails, I believe, is that he bases his argument on the definition the ampere being a ‘coulomb per second’. If this were to be the case, 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 (well, not in modern times anyway!) and, so, the ampere is not reliant on, and thus ‘less fundamental’ than, the coulomb.

So, how is the ampere defined? Well, there are three ‘effects’ of an electric current: the heating effect, the chemical effect, and the magnetic effect. Theoretically, any 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:

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’.

But things are about to change (or, by now, will have changed!)! Because, it has been proposed that, from 2019, the ampere should be defined in terms of the rate of flow of elementary charges —such as those carried by individual electrons or protons.

This proposed change would define an ampere as being ‘the current in the direction of flow of a particular number of elementary charges per second’.

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 can be argued 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 it is an SI base unit, and has never been defined in terms of the coulomb (a derived unit) but, from 1947, in terms of the force between energised conductors and, from 2019, in terms of the flow of individual elementary particles.

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