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The fact that two balls charged with 1 coulomb each would repel/attract each other from a distance of 1 metre with a force sufficient to lift the Seawise Giant would suggest me otherwise, but has anyone ever charged an object with 1 coulomb of net charge?

Why was such a ridiculously large charge chosen as the unit of charge? Or better, why did we give the Coulomb constant such a big value instead of using a value in the same order of magnitude of the Newton constant ($10^{-11}$)?

EDIT

For the historical reasons that explain why the coulomb was chosen as the unit of charge please refer to the good answers given to this question.

After a bit of research I have found that the highest voltage ever created is $32\,\mathrm{MV}$ at the Oak Ridge National Laboratory. With such a voltage the best we can do is charging a copper sphere the size of a basketball with around 424 microcoulombs:

$$Q = 32 \times 10^6\,\mathrm{V} \times 4\pi\epsilon_0 \times 0.119\,\mathrm{m} = 4.237 \times 10^{-4}\,\mathrm{C}$$

Such a sphere, when placed at a distance of $1\,\mathrm{m}$ from the surface of a similarly charged sphere, would experience a repulsion of $1052\,\mathrm{N}$ (the force needed to lift $107\,\mathrm{kg}$).

If the maximum voltage we can access is $32\,\mathrm{MV}$ and we want to charge a sphere with $1\,\mathrm{C}$, all we need is a sphere $561.7\,\mathrm{m}$ in diameter. It might often snow on the top.

moonblink
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  • The edit you made clarifies your question, but also invalidates some of the existing, interesting answers. Perhaps it would make sense for you to revert the edit and ask another question about net charge? – user1079505 Jan 02 '22 at 00:04
  • A lot of Planck units--which enable the most fundamental physical constants to have a value of 1--are even more wildly outside the range of day-to-day use. – EvilSnack Jan 02 '22 at 01:51
  • @user1079505 A charge is always a net charge. Other usages are improper ways of expressing an energy omitting the volts. – moonblink Jan 02 '22 at 02:05
  • @EvilSnack If you think that at all objects tend to be electrically neutral the Planck charge is way more “everyday life” than the coulomb. The Planck mass is also not so bad. Rubbing a balloon with wool cloth can easily charge it with around $10^{-14},\mathrm{C}$. The same charge in Planck units will be about $5330,\mathrm{q_P}$. – moonblink Jan 02 '22 at 04:14
  • @moonblink well, it's a bit of a linguistic thing. In a capacitor charge can be moved from one conductor to another, and it is called "charge stored in a capacitor" and the process is called "charging". Anyway, for absolute charge, LHC proton beam went up to something like 5·10⁻⁵C and further upgrades are planned. I wonder how does Tokamak compare to that? This question: https://physics.stackexchange.com/questions/73763 suggest stars can gain charge measured in Coulombs. – user1079505 Jan 03 '22 at 17:59
  • @user1079505 The biggest linguisting thing for me is the fact that either people don't realize how big one coulomb is, or when they do, they attribute its weird strength to the strength of electromagnetism. But the fact for me is that we chose a huge unit for the charge, which is out of our range (we aren't even able to put one coulomb together in a laboratory in 2022). It's like as if we decided to choose a dozen megatonnes as the unit of mass. – moonblink Jan 04 '22 at 00:29

6 Answers6

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Actually the ampere (SI unit for electric current) was defined first (in 1881, see Wikipedia: Ampere - History). They chose this size for $1$ ampere, probably because at this time such a current could be produced with a decent electrochemical battery, and was easily measurable with a galvanometer by its magnetic effect.

The natural consequence of this is: A flowing charge of $1$ coulomb (i.e. a current of $1$ ampere flowing for $1$ second) is also a convenient unit, neither ridiculously large nor ridiculously small.

The fact, that a static charge of $1$ coulomb is a really big thing, is an entirely different story, which has to do with the large electric force between charges.

Thomas Fritsch
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Has anyone charged an object with 1 coulomb?
Not a problem nowadays with supercapacitors.

Why was such a ridiculously large charge chosen as the unit of charge?
Once the second and the ampere (both reasonable units) have been chosen what else can one do.
It so happens that when dealing with electrostatics a coulomb is a large unit but that is not so in the context of current electricity.
Another example is the tesla which for most situation is a very large unit.

Farcher
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    What else can one do? Hypothetically, one could define the equations of electromagnetism to have both the current and the charge as base units, and define the coulomb independently from the ampere, e.g. $I = k,\mathrm{d}q/\mathrm{d}t$, where the definitional constant $k$ would have to be measured by an experiment linking the two units. But, indeed, this would be much impractical (especially in the current SI where the units are defined through fundamental constants). – Massimo Ortolano Dec 30 '21 at 11:29
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    @MassimoOrtolano or define the Coulomb and the Ampere and make the second into a derived unit! – Javier Dec 30 '21 at 13:31
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    Couldn't they just have for example used the Microcoulomb as the Coulomb, $1, \mathrm{C}' = 10^{-6} ,\mathrm{C}_\mathrm{SI} = 10^{-6} ,\mathrm{As}$ ? I think the real answer is, charge values were rarely used in everyday life, so it wasn't a priority to make the unit have a nice value. – jdm Dec 30 '21 at 17:03
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    @jdm That would make the unit system noncoherent, violating a basic principle of SI. – nanoman Dec 30 '21 at 23:09
  • @MassimoOrtolano Nice joke ! LOL – Alfred Dec 31 '21 at 03:39
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    @nanoman yeah, it would be almost as bad as if they made the base unit of mass the kilogram instead of the gram, and then for some reason the unit of volume was the cube of the decimeter instead of the meter. – hobbs Dec 31 '21 at 07:38
  • @nanoman Science is full of convenience constants, like the mol or radian. Particle physicists like to redefine energy, length, and so on to be dimensionless (and in an abuse of terminology say we "set" $\hbar = c = 1$). We also use eV instead of Joule. My point is just that if people had to deal with charge values a lot and the SI prefixes were too cumbersome, they could either define a "nicecoulomb" $\mathrm{C}'$ unit or maybe use "nicecharge" $Q' = 10^6 Q$ instead. But apparently this is not an issue. – jdm Jan 02 '22 at 10:12
  • @jdm The nicecoulomb exists; we just call it μC. :) Prefixes aren't too cumbersome; this is why we have them. – nanoman Jan 02 '22 at 10:27
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The underlying reason that 1 coulomb seems like a large amount of charge is that most charged particles in ordinary settings are nonrelativistic -- moving at speeds $v$ much less than the speed of light $c$. Compared to electrostatic forces, magnetic forces are smaller by a factor $v^2/c^2 \ll 1$.

Thus, to obtain significant magnetic forces requires large amounts of charge to make up for the slow motion. And to keep the magnetic forces from being overwhelmed by electrostatic forces, the charges must be balanced by opposite, differently moving charges -- e.g., moving electrons balanced by stationary ions in a wire.

Thus, in a coherent system of units, it is inevitable that either the magnetic effects of a unit current are very weak (as in ESU), or the electrostatic effects of an unbalanced unit charge are very strong (as in EMU and SI).

Empirically establishing the relation between electrostatic and magnetic effects of a given amount of charge is nontrivial, requiring experiments with a high "dynamic range". This can be seen because it is effectively a way of measuring the speed of light, which is at least 6 orders of magnitude away from most commonly measured phenomena.

As it happened, both the electrical experiments (effectively linking ESU and EMU) and the direct measurement of the speed of light had already been performed to sufficient precision by 1861, when Maxwell was able to compare the numbers and reach the stunning conclusion that the speed of light is an inherent property of electromagnetism.

nanoman
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No matter what unit you choose, it's unreasonable for some purpose. For electrochemists, a coulomb is only $10^{-5}$ moles of singly-charged ions, not much. But for electrical machinery, coulombs/second (amperes) is a practical unit. The circuit breakers in your house trip at modest numbers of amperes.

These SI units are common in engineering, but there are other systems around. You might find ESU or Gaussian units more comfortable for electrostatics.

Buzz
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John Doty
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    “A coulomb is only $10^{-5}$ moles of singly-charged ions, not much”: Not much?? A $6,\mathrm{mm}$ drop containing $10^{-5}$ moles of singly-charged ions of water will explode with an energy in the order of $10^{12},\mathrm{J}$, which is 1 kiloton of TNT. – moonblink Dec 31 '21 at 02:47
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    A gram of anything contains roughly $6 \times 10^{23}$ protons and a similar number of electrons (remembering that in some sense a neutron contains a proton and an electron). This is a little under $10^5$ coulomb. In this context the coulomb is indeed quite small; the problems arise not from having coulombs of charge around but from having coulombs of unbalanced charge. – Peter Dec 31 '21 at 11:07
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    @moonblink In an electrochemistry context, your drop of water containing a coulomb of, say, H+ ions would also contain a coulomb of negative ions, perhaps Cl-. A weak hydrochloric acid solution in this case. – John Doty Dec 31 '21 at 13:15
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    I think it would have been nice to define a coulomb as one mol of electrons. Or maybe, as it would have been nice to have the kilogram an SI base unit without prefix, make it one kilomol ;-). – Peter - Reinstate Monica Dec 31 '21 at 15:13
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    @Peter In your $6 \times 10^{23}$ protons + $6 \times 10^{23}$ electrons example the number of coulombs is zero. A coulomb does not count objects, it is a unit of charge. Two opposite charges have zero charge. – moonblink Dec 31 '21 at 19:58
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The plates of "large" capacitors often receive charges exceeding 1 coulomb.

This 5V capable, 1 Farad capcator is about 5mm thick 20mm diameter and costs a few dollars Cornell-Dubilier EDC334Z5R5V

However it's not an isolated charge, one plate of the capacitor accepts a charge as the opposite charge is induced in the other plate (the plates are convoluted structures internal to the case pictured)

Jasen
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    Ok, I'll take the bait: If 1 coulomb on 2 separate balls could make enough force to lift the Seawise Giant, how does this capacitor hold 1 coulomb without self-destructing? (I guess it has to do with the convoluted internal structures of the plates, or maybe someone got a unit wrong somewhere?) – krubo Jan 01 '22 at 20:06
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    @krubo See https://physics.stackexchange.com/q/685924/264705 – moonblink Jan 02 '22 at 01:10
  • a capacitor has two plates with opposite charges, so the net charges is nearly zero because when one plates is +1 C the other is -1 C – Jasen Jan 02 '22 at 03:51
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A typical tractor battery holds a charge of 120Ah = 432000C. And since the starter motor can draw something like 800A and the tractor does not start right away every time (and you need to pre-glow at lower but still non-trivial current for a minute when it's cold, when the battery does not have full capacity anyway), a Coulomb is kind of a ridiculously small charge unit.

And that's small potatoes compared to what a modern electric car throws around in charge.

What is small and large is relative.

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    It's incredible how many people – even with a scientific background – have problems understanding how electricity works and and how big one coulomb is. If a tractor battery held 432000 C of net charge it would explode with an energy equivalent to 50 Hiroshima nuclear bombs. Why does it not happen? Obviously a tractor battery's net charge is zero. – moonblink Dec 31 '21 at 02:28
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    @moonblink People always underestimate just how strong electro-magnetism is, especially electro-statics. It doesn't help when schools tend to reinforce the practice of naïvely applying equations or comparing units without understanding the context in which those make sense. Or thinking that batteries are just large capacitors. But there is a kernel of an answer, if you correct the flawed thinking - coulombs are a fine unit for moving charges, or the kind of static charge that was of much interest in early study of electricity - like the kind that produces lightning. – Luaan Dec 31 '21 at 11:23
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    @moonblink The problem is that you didn't specify clearly enough what you meant by "charging an object". I think this is an okay answer for the question as posed and it gives an example of a case where 1 Coloumb is not a ridiculously large amount (although 1 Coloumb is not referring to the net charge of a macroscopic object in this case). – jkej Dec 31 '21 at 11:58
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    @moonblink the problem is that battery capacity is more often than not stated in "Amp hours" not Joules as it should be. Also in the RV world most people think that batteries store "amps" and charge at a rate of "amps per hour", so try telling them that batteries don't store charge... (one day I will do a YT video to address this) – Rodney Dec 31 '21 at 12:19
  • @Luaan Are you trying to say that the net charge of a capacitor is not zero? From the outside a battery is indeed somewhat like a capacitor, and with electrochemical supercapacitors the boundary is fairly fuzzy. – Peter - Reinstate Monica Dec 31 '21 at 15:20
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    This is a fair answer and says nothing else than the two highest-voted answers: That in terms of flowing charges a Coulomb is not large. – Peter - Reinstate Monica Dec 31 '21 at 15:22
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    @jkej I have edited the question to make it more clear now. – moonblink Dec 31 '21 at 20:01
  • @Rodney I agree completely! – moonblink Dec 31 '21 at 20:03
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    @moonblink The energy stored in the battery is 432 kC · 12 V is 5 MJ. The bomb released 70 TJ. – user1079505 Jan 01 '22 at 23:03
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    @user1079505 We are talking about two different things. The battery does not hold $432,\mathrm{kC}$ of charge, but holds $432,\mathrm{kC}\times12,\mathrm{V}$ of energy – in fact the battery holds exactly zero charge. It's like comparing “5 balls” with “5 balls on a cliff ready to fall”: in the first case I am expressing a mass, in the second case I am expressing an energy. A sphere charged with $Q=1,\mathrm{C}$ will explode with an energy equal to $E=k_e\frac{Q^2}{r}$, while an object storing $432,\mathrm{kC}\times12,\mathrm{V}$ of energy can explode at most with that energy. – moonblink Jan 02 '22 at 00:24