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Magnetic field and π

by Amir H.Saba
Tags: π, field, magnetic
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Amir H.Saba
#1
Mar8-12, 11:33 AM
P: 2
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 ?
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tiny-tim
#2
Mar8-12, 12:46 PM
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Hi Amir! Welcome to PF!
From the PF Library on magnetic field
What is 0?

o 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 o = 1 N/A2 (so that it needn't be mentioned)?

well, it would be , buuuut

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

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!

so, for practical convenience only, we make o 107 smaller, and the amp 107 larger!

(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 o 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 1/0c, = 107/4πc C/Nm (or F/m).)
Amir H.Saba
#3
Mar8-12, 02:57 PM
P: 2
yes, your sentences is true ,but my query is that π is a number that related to sphere.but o is a constant that related to environment.and why is a special number that has π ?
o 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 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.

tiny-tim
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Mar8-12, 03:06 PM
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Magnetic field and π

Quote Quote by Amir H.Saba View Post
yes, your sentences is true ,but my query is that π is a number that related to sphere.but o is a constant that related to environment.and why is a special number that has π ?
No, o is not related to the environment.

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

(of course, (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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