actually, i think it did its time, the very first professional experiment that lead people to believe existence of magnetic force so magnetic field,(the experiment of Ampere's about that force). It is too small to be applied and so small that it is never a problem like eddy currents.
and besides i don't think it can be thought separately, after all it is a force that is by a magnetic field and a current, if you think so, motors are also an application of it, magnetic field is there is produced by nothing but a lot of currents we can think it as a strong current, but i thought you ask spesifically the equation F=I1I2(mu)/2(pi)r so i was against gneill.