Consider a surface S, like the one shown below.  Ampère's Law for steady currents and fields states that the integral of B*dl around a closed path C that surrounds the surface is related to the net current that passes through the surface S by

B*dl = μ0*(±I1 ± I2 ± …)

The sign associated with each current is determined by an application of the right-hand rule.  When the fingers of the right hand are curled in the direction of the integration around the closed path C the thumb of the right hand will point in the direction of positive current.  Using this rule, I1 in the figure below will have a positive sign and I2 will have a negative sign when one constructs the sum of currents on the right-hand side of Ampère's Law. 

surface with two currents going through it.

Ampère's Law is often used to calculate expressions for magnetic fields in cases of high symmetry like finding the magnetic field due to a long, straight current carrying wire.


Last modified: Sat Jul 8 22:40:58 EDT 2006