The vacuum permeability, or the capability of the vacuum to permit magnetic field lines, contains the value of π. Why? What does this have to do with the ratio of a circle's circumference to its diameter?
Answer
This is nothing but a choice of units.
Let me make that (hopefully) more clear by explaining more about how choosing units in electromagnetism works:
Coulomb's Law is →F=kq1q2r2ˆ→r for the force between two charges q1 and q2. k is different in the various systems of units - essentially, it depends on how the unit of charge is defined.
Ampere's Law is →F=k′I1I2∮C1∮C2d→r1×(d→r2×→r)|r|3 for the force between two currents along C1 and C2. k′ is different in the various systems of units - essentially, it depends on how the unit of current is defined.
In electrodynamics, we find out that k/k′=c2
Now we introduce constants μ0=4πk′,ε0=14πk
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