# Magnetic field and π

1. Mar 8, 2012

### Amir H.Saba

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. Mar 8, 2012

### tiny-tim

Welcome to PF!

Hi Amir! Welcome to PF!

From the PF Library on magnetic field …​

What is µ0?

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

Why isn't µo = 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! :yuck: …

so, for practical convenience only, we make µo 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 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), $\varepsilon_o$, is defined as 1/µ0c², = 107/4πc² C²/Nm² (or F/m).)

3. Mar 8, 2012

### Amir H.Saba

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.

4. Mar 8, 2012

### tiny-tim

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).