Magnetic field and π

  1. Hi
    as you know according to ampere's law ∫B.dl=μ0I
    but why μ0 that appears in Maxwell's equations is exactly 4π *10-7 ?
    for example in electric field ε0 is 8.85 *10-12
    and μ0 like ε0 is a constant that is related to material properties and why this constant is a special number as π that B is special ?
     
  2. jcsd
  3. tiny-tim

    tiny-tim 26,041
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Amir! Welcome to PF! :smile:

    From the PF Library on magnetic field …​

    What is µ0?

    µo is the conversion factor between tesla ([itex]T\ =\ N/A.m[/itex]) and amp-turns per metre ([itex]A/m[/itex]): so it has units of [itex]N/A^2[/itex].

    Why isn't µo = 1 N/A2 (so that it needn't be mentioned)? :confused:

    well, it would be :smile:, buuuut :rolleyes:

    i] in SI units, a factor of 4π keeps cropping up! … so we multiply by 4π :wink:

    ii] that would make the amp that current which in a pair of wires a metre apart would produce a force between them of 2 N/m …

    which would make most electrical appliances run on micro-amps! :yuck: …

    so, for practical convenience only, we make µo 107 smaller, and the amp 107 larger! :biggrin:

    (so the amp is that current which in a pair of wires a metre apart would produce a force between them of 2 10-7 N/m, and µo is 4π 10-7 N/A2 (= 4π 10-7 H/m))

    (for historical details, see http://en.wikipedia.org/wiki/Magnetic_constant)

    (And the electric constant (permittivity of free space), [itex]\varepsilon_o[/itex], is defined as 1/µ0c², = 107/4πc² C²/Nm² (or F/m).)
     
  4. yes, your sentences is true ,but my query is that π is a number that related to sphere.but µo is a constant that related to environment.and why is a special number that has π ?
    µo is exactly 4π 10^-7 but if it is a constant about environment , why it is exactly a special number ? I think it should related to microscopic vacuum properties ,if isn't it ,why for other environments µ is not 4π *10^-7 ? and is a other number? but for free space is a special number like π !
    sorry for my english is not good.
     
  5. tiny-tim

    tiny-tim 26,041
    Science Advisor
    Homework Helper

    No, µo is not related to the environment.

    µo is simply the conversion factor between tesla and amp-turns per metre.

    (of course, µ (for a material) is related to the material)

    The 4π is a standard factor in SI units, since it naturally relates the strength of a source to its flux (because the field from the source spread out over an area 4πr2 instead of r2).
     
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