Dimensional Units for Coulomb in SI

[T0mr]

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.

 

[ModusPwnd]

Put amps in terms of coulomb. One amp is a coulomb per second isn't it? Look that up to make sure.

 

[T0mr]

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.

 

[Jimmy]

The Ampere is a base SI unit.

http://en.wikipedia.org/wiki/SI_base_unit

 

[T0mr]

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]

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]

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]

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

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

 

[DrClaude]

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

I always express mass in kg

 

[T0mr]

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.

 

[Gordianus]

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]

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.

 

[T0mr]

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]

I am getting equations like this:

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

Then that equation is wrong.

 

[Dale]

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.

 

[physwizard]

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

 

[Borek]

Coulomb is also a fundamental unit

No, it is derived - 1C=1A×1s.

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

 

[physwizard]

No, it is derived - 1C=1A×1s

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

 

[Borek]

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

 

[technician]

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

?how so ??

 

[T0mr]

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]

?how so ??

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

 

[technician]

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

How is this helpful?
You can't express s as kg...is that any better...random examples of what cannot be done ??

 

[Borek]

How is this helpful?
You can't 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.

 

[technician]

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

 

[mikeph]

I found it useful. metres and kilograms are slightly less abstract than amperes.

 

[technician]

Glad to have been of help in the value of analogies

 

[Dale]

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.

Yes, it does. If you are using the Ampere then you are using the SI convention, since that is where the Ampere is defined, and the SI convention specifically states that the base quantities are mutually independent.

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.)

There is never any way to prove that a set of definitions is self-consistent, that is the punchline of Goedel's theorem. However, mere lack of a proof of consistency is not itself a proof of inconsistency. There is no indication in any of the scientific literature that the SI units are not self consistent. So it is pure speculation to think about the SI being inconsistent.

The bottom line is that your formula is WRONG in SI units. The remote possibility that a completely undiscovered flaw in the SI system might miraculously save the formula at some future date is not a justification today for accepting a formula that is known to be wrong under current science.

Did you look into the cgs units as I have suggested 3 times now? In cgs the statcoulomb is equal to $1 g^{1/2} cm^{3/2} s^{-1}$. Your specific formula is still wrong in cgs, but at least what you are trying to do can be done in those units. You just have to change all of your physics equations that involve charge.

 

[T0mr]

Yes, it does. If you are using the Ampere then you are using the SI convention, since that is where the Ampere is defined, and the SI convention specifically states that the base quantities are mutually independent.

In fairness, the SI convention would work exactly like it does now without defining the base quantities to be mutually independent. So it is in no way critical or damaging to the convention to not assume that m, kg, s, A must be independent of each other. That definition if not accompanied by some kind of proof is an assumption, and if everyone is operating under the same assumption then nothing new will come of it.

However, mere lack of a proof of consistency is not itself a proof of inconsistency. There is no indication in any of the scientific literature that the SI units are not self consistent. So it is pure speculation to think about the SI being inconsistent.

I completely agree that these definitions may well be consistent. But I have no way to know or even to give odds about the truth of the statement that those base units must actually be mutually independent.

But as you have mentioned, if there is nothing in the scientific literature about a possible way to rewrite Amperes in terms of the other units then I will not force this issue. I just thought it might be worth it to ask and see if any good dimensional formula existed. I appreciate your time and I will look into using cgs on some of the equations. Thank you.

 

[makrisj]

http://www.phys.ufl.edu/courses/phy2049/sum14/Dimensional-2049-Ramond.pdf

Coulomb has dimensions of [M]^1/2 * [L]^3/2 * [T]^-1

It's easy to figure this out, since coulomb's law is an equation having Newtons on left side and Ke*C^2/m^2 on the other. Easily derived by dimensional analysis.
I was looking for it (too bored to derive it myself) and I came into that argument, and thought I could help a bit.

 

[SteamKing]

Yes, but the argument is more than two years old. PF discourages reviving old threads (a practice which is called necro-posting.)

You can, however, start your own thread, and refer to another thread, if you wish.

 

[Dale]

Coulomb has dimensions of [M]^1/2 * [L]^3/2 * [T]^-1

No, it doesn't. See the official BIPM page: http://www.bipm.org/en/measurement-units/base-units.html

Yes, but the argument is more than two years old. PF discourages reviving old threads (a practice which is called necro-posting.)

You can, however, start your own thread, and refer to another thread, if you wish.

Yes. Thread closed.