# What are the actual electromagnetic units in the foot-pound-second (FPS) system?

So I've been reading this Wikipedia article, and I came across the cited note that someone has derived the electromagnetic units for the FPS system. However, I can't find that publication so does anyone have a clue as to what are the actual names for the units proposed by Stephen Drenser in the fpse and fpsm systems?

• Can't ever recall seeing any electromagnetic quantities described in any sort of FPS units. Are you asking just out of curiosity?
– user93237
Jul 26, 2017 at 19:54
• Pretty much. It's just that the FPS system is quite fine for problems in mechanics and I'm writing simulation code based on it, and I was wondering whether there is a standard way to extend that to electromagnetics. Jul 26, 2017 at 19:59
• Look here and the references. en.wikipedia.org/wiki/Foot–pound–second_system#Electromagnetic_units Jul 27, 2017 at 6:32
• That's like the exact same article under the link in the original question :) Nevertheless, does that mean that I can call the units the same as the CGS units and just mention somewhere that they are defined otherwise? Jul 27, 2017 at 6:52

In esu cgs units the statcoulomb is defined such that "If two stationary objects each carry a charge of 1 statC and are 1 cm apart in vacuum, they will electrically repel each other with a force of 1 dyne." Using the SI equation $${\displaystyle F={\frac {q_{1}q_{2}}{4\pi \epsilon _{0}r^{2}}}} (SI),$$ and substituting F $= 1$ dyne $= 10^{−5}$ N, and $r = 1$ cm $= 10^{−2}$ m, solving for $q = q_1 = q_2$, the result is $q = (1/2997924580)$ C $\approx 3.34 \times 10^{−10}$ C. Therefore, an object with a charge of 1 statC has a charge of $3.34 \times 10^{−10}$ C.
Presumably you would define the "Imperial Coulomb" by defining it as the force of 1 lb ft/s$^2$ between two unit charges placed 1 foot apart? Given that the speed of light is approximately 1 foot/ns this mightn't be such a dumb thing to do? Well, actually, yes it would!