Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Dimensional Units for Coulomb in SI

  1. May 22, 2013 #1
    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.
     
  2. jcsd
  3. May 22, 2013 #2
    Put amps in terms of coulomb. One amp is a coulomb per second isnt it? Look that up to make sure.
     
  4. May 22, 2013 #3
    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.
     
  5. May 22, 2013 #4
  6. May 22, 2013 #5
    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.
     
  7. May 22, 2013 #6

    davenn

    User Avatar
    Science Advisor
    Gold Member

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


    Dave
     
  8. May 22, 2013 #7

    Dale

    Staff: Mentor

    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.
     
  9. May 22, 2013 #8

    Borek

    User Avatar

    Staff: Mentor

    It is like asking for a formula for m in terms of kg.
     
  10. May 22, 2013 #9

    DrClaude

    User Avatar

    Staff: Mentor

    I always express mass in kg :biggrin:
     
  11. May 22, 2013 #10
    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.
     
  12. May 22, 2013 #11
    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.
     
  13. May 22, 2013 #12

    f95toli

    User Avatar
    Science Advisor
    Gold Member

    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.
     
  14. May 22, 2013 #13
    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.
     
  15. May 22, 2013 #14

    Dale

    Staff: Mentor

    Then that equation is wrong.
     
  16. May 22, 2013 #15

    Dale

    Staff: Mentor

    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.
     
    Last edited: May 22, 2013
  17. May 22, 2013 #16
    Coulomb is also a fundamental unit, like those for length, mass and time.
     
  18. May 22, 2013 #17

    Borek

    User Avatar

    Staff: Mentor

    No, it is derived - 1C=1A×1s.

    Unless we are thinking about something else when we say "fundamental".
     
  19. May 22, 2013 #18
    I could say that the ampere was derived.
    I A = 1C / 1s .
     
  20. May 22, 2013 #19

    Borek

    User Avatar

    Staff: Mentor

    I am not sure how it was historically, but as of today, Ampere is a basic unit - by definition.
     
  21. May 22, 2013 #20
    ?????how so ???????
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Dimensional Units for Coulomb in SI
  1. Gaussian vs SI units (Replies: 2)

  2. Newton's SI Units (Replies: 3)

  3. Si units (Replies: 1)

Loading...