The Permeability of Free Space μ0
How is the Permeability of Free Space μ0 defined? First we need to define the Ampere as
this constitutes the magnetising force in a conductor.
“One Ampere is that current which if maintained in
two straight parallel conductors of infinite length, and
negligible csa, placed one metre apart will produce a
force between them of 2*10-7 Newtons per metre of
length”*
th
* Electrical technology 5 edition Edward Hughes 1985 page 6
If we imagine an infinitely short wire then the
Magnetising force is 1 amp.
The length of the flux line is 2π hence the magnetic field strength at 1 metre is 1/2 π amps
per metre.
We know that the force on a conductor is given by:
F=BiL newtons so the force per metre length is B[T] * 1[m] * 1[A] = B newtons
We also know that the Ampere as defined gives 2*10-7 Newtons at one metre from 1 amp
So B = 2*10-7 T this is the flux density at point C
This is a measure of how much Magnetic flux is produced for a given amount of magnetic
field strength and is therefore how magnetisable a vacuum is.
The answer, μ0 = 4 π*10-7 (units are Henrys per Metre)
But not all things give the same magnetic flux density for a given magnetic field strength.
Some materials concentrate the flux to give greater flux density. So other materials have a
permeability relative to μ0. To calculate the permeability of material all we need are the
figures for B and H.
The Absolute Permeability of a material is B/H (flux density/magnetising force)
We can find the Absolute Permeability of something by multiplying μ0 by μr