# Dimensional Units for Coulomb in SI

Does anyone know of a dimensional formula for the Coulomb in SI that does not involve amperes as in A*s? I am looking at some equations and the dimensional analysis is leaving me with C (Coulomb unit charge) and left over m, kg, s to various powers. Just curious if anyone has come across some relationship that might not be well known but is logically sound. Prefer if formula was in SI base units. Thanks.

Put amps in terms of coulomb. One amp is a coulomb per second isnt it? Look that up to make sure.

I can write C = A*s and/or A = C/s but unless I have a dimensional formula for Coulomb or Amperes in terms of m, kg, s nothing is going to happen.

I understand the Ampere is defined as a base unit but the equations I am working on might not know that. So if anyone out there has come across a formula for the Coulomb in terms of m, kg, s that would be greatly appreciated.

davenn
Gold Member
I understand the Ampere is defined as a base unit but the equations I am working on might not know that. So if anyone out there has come across a formula for the Coulomb in terms of m, kg, s that would be greatly appreciated.

they are not related ... what are you trying to do ?

Dave

Dale
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2020 Award
I understand the Ampere is defined as a base unit but the equations I am working on might not know that. So if anyone out there has come across a formula for the Coulomb in terms of m, kg, s that would be greatly appreciated.
In SI there is no way to write a dimensionally consistent equation with only C on one side and only powers of m, kg, and s on the other side. This is what it means for a unit to be a base unit, as Jimmy said.

In the cgs system the Statcoulomb is a derived unit, but Maxwells equations are different in cgs units than in SI.

Borek
Mentor
formula for the Coulomb in terms of m, kg, s

It is like asking for a formula for m in terms of kg.

DrClaude
Mentor
It is like asking for a formula for m in terms of kg.
I always express mass in kg I am getting equations like this:

m = (kg^5*s^3)/(C^4*m^4)

That means C would have to have units ((kg^5*s^3)/m^5)^(1/4) for the equation to be dimensionally correct in this case. It seems to be the consensus that it is not posssible to write the coulomb in any other way than A*s. I completely get that writting kg in terms of m and s seems impossible. But is there a formal proof that what we call a kilogram cannot be expressed in terms of other base units somehow. I am more inclined to accept that kg cannot be written in terms of m and s without some kind of proof. But something about the Ampere makes me question it.

Here goes an alternative way:

Consider two infinitely long parallel wires 1 meter apart. If each wire carries 1 A then the force between wires per meter of wire is 2 10-7 N. This way you skip the Coulomb.

f95toli
Gold Member
But is there a formal proof that what we call a kilogram cannot be expressed in terms of other base units somehow. I am more inclined to accept that kg cannot be written in terms of m and s without some kind of proof. But something about the Ampere makes me question it.

You can't "prove" anything about the SI; the SI is an agreement; that the Ampere is a base unit is something that has was decided by voting at the General Conference on Weights and Measures. Hence. there is nothing "fundamental" about our choice of base units: they can -and have- changed several times.
The whole point of the SI is that it is a practical and -reasonably- self consistent system of units that is used internationally.

If you cannot prove that the Ampere could be written as a function of m, kg, and s, then it might be possible to do so? I do understand that the SI units are a convention determined by people. That does not necessarily mean that proof could not exist to verify that these base units must be independent of each other.

Dale
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2020 Award
I am getting equations like this:

m = (kg^5*s^3)/(C^4*m^4)
Then that equation is wrong.

Dale
Mentor
2020 Award
If you cannot prove that the Ampere could be written as a function of m, kg, and s, then it might be possible to do so? I do understand that the SI units are a convention determined by people. That does not necessarily mean that proof could not exist to verify that these base units must be independent of each other.
There is a proof, it is very simple:

The Ampere is a base unit by definition of Ampere. (as agreed by vote)
Base units cannot be written in terms of other base units by definition of base unit.
Therefore, the Ampere cannot be written in terms of other base units.
QED.

Again, you can do this in cgs units, not SI units. But that changes the physics equations.

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Coulomb is also a fundamental unit, like those for length, mass and time.

Borek
Mentor
Coulomb is also a fundamental unit

No, it is derived - 1C=1A×1s.

Unless we are thinking about something else when we say "fundamental".

No, it is derived - 1C=1A×1s

I could say that the ampere was derived.
I A = 1C / 1s .

Borek
Mentor
I am not sure how it was historically, but as of today, Ampere is a basic unit - by definition.

It is like asking for a formula for m in terms of kg.

?????how so ???????

DaleSpam said:
There is a proof, it is very simple:

The Ampere is a base unit by definition of Ampere. (as agreed by vote)
Base units cannot be written in terms of other base units by definition of base unit.
Therefore, the Ampere cannot be written in terms of other base units.
QED.

Just because the Ampere was defined to be a base unit does not mean that it cannot be defined in terms of other base units. Even if everyone in the world agrees that the Ampere is a base unit, and that by the definition of the base unit the base unit cannot be written in terms of other base units, without a rigorous proof there is no way to know with certainty that the set of definitions is logically consistent (meaning that the definitions do not contradict each other.)

For example imagine there are only two units: the star unit and the atom unit. We define these two units to be base units because we do not notice for some reason that stars are made of atoms. We define the base unit to mean a unit that cannot be defined in terms of other base units, and so we have created a logically inconsistent set of definitions.

Borek
Mentor
?????how so ???????

You can't express charge using m/kg/s just like you can't express meters using kilograms.

You can't express charge using m/kg/s just like you can't express meters using kilograms.
You cant express s as kg....is that any better....random examples of what cannot be done ??

Borek
Mentor
You cant express s as kg....is that any better....random examples of what cannot be done ??

It was an analogy. From what OP stated he was aware of the fact kg/m/s are independent units, and I was showing him how he wants to do something impossible, using example that he should understand.

s as kg would work exactly the same, but we are derailing the thread.

It was an analogy. From what OP stated he was aware of the fact kg/m/s are independent units, and I was showing him how he wants to do something impossible, using example that he should understand.

s as kg would work exactly the same, but we are derailing the thread.

Mine was also an analogy....you are correct...the thread is being derailed by an analogy that is no use/help