Ampère's Law

In Electrostatics we have seen that charges produce electric fields. The electric field can be calculated via Gauss' Law:

· d

= q / $\epsilon$₀

where q is the charge enclosed in the closed surface with area A, and $\epsilon$₀ is the permittivity of free space (here we only use the vacuum value for now).

Moving charges (currents) produce magnetic fields. This relationship between the current, I, and the magnetic field, B, is given by Ampere's Law:

· d

= I µ₀

where the integration is along any closed path that enclosed the current I.

The constant µ₀has the (exact, by definition!) numerical value

µ₀= 4$\pi$ · 10^-7 Tm/A

and is called the permeability of free space.

We will not use the above general form of Ampère's law, but instead derive special cases that have simple symmetries. Then Ampère's law can be used to find the magnetic field produced by currents in these special cases which have symmetry as is described in the following.