Ampere's Law

Pre: Current Density

Consider a wire which has been bent into a loop. Then:

Law

(see integral, B-field, dot product)

We call the loop an Amperian loop, and it acts as a boundary, similar to a Gaussian surface. For Ampere's law, the shape of the loop does not matter, as long as it is closed.

Similar to Gauss's law, if we can create a mathematical loop over which we can guarantee one of the following:

  1. is in the direction of throughout the loop and is a constant through out the loop
  2. is 0 in parts where is constant (i.e OR )

then we can use Ampere's law to calculate the magnetic field for the current distribution.

With these conditions met, we have: