Re: How was the permeability (vacuum) value arrived at?

Eric,

The value of mu_0 is defined to satisfy the magnetic portion of Maxwell's Equations. I don't know how to represent the math in HTML, so you should look at the equations in the above link as a reference.

Anyway, the first of Maxwell's equations for magnetism is that the divergence of the magnetic field ("del-dot-B") equals zero. This simply means that there are no magnetic charges. If you enclose any portion of space within a surface, the number of magnetic field lines going in equals the number coming out. Easy.

The second magnetism equation describes the curl of the magnetic field:

                         dE
del x B = mu_0 epsilon_0 -- + mu_0 J
                         dt

mu_0 is a very convenient constant, selected to be exactly 4 pi x 10^-7 Newtons/(Ampere^2). It is used simply to match the units of current and force. Epsilon_0, as you already know, is an experimentally derived constant.

I hope this helps.

Cheers,

Sam Silverstein