A wire carrying a current will generate a magnetic field whose direction is given by the right hand grip rule.
If in the presence of this magnetic field any other conductor carrying a current will experience a force. The magnetic field generated by a wire carrying a current I-1 has magnitude
(1) at radial distance
from the wire. The Biot Savat gives the force acting on a length
of conductor carrying a current
as
.
is at right angles to wire 2 everywhere we can write
Substitute (1) into this expression to obtain
or
Application of he left hand rule tells us that if the currents travel in the same direction the force is attractive and if the current is in the opposite direction the force is repulsive.