FORCE BETWEEN DIFFERENTIAL CURRENT ELEMENTS
The concept of the magnetic field was introduced to break into two parts the problem of finding the interaction of
one current distribution on a second current distribution. It is possible to express the force on one current element
directly in terms of a second current element without finding the magnetic field. Because we claimed that the
magnetic-field concept simplifies our work, it then behooves us to show that avoidance of this intermediate step
leads to more complicated expressions.
The magnetic field at point 2 due to a current element at point 1 was found to be
