©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’ the **ampere** is 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… * 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 textbooks 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 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*.