Approximate formula for the eddy-current loss induced in a long conductor of rectangular cross-section by a transverse magnetic field

A formula is derived for the eddy-current loss produced in a long conductor of rectangular cross-section, with dimensions not exceeding 6 times the skin depth of the material, by a transverse magnetic field which varies sinusoidally with time. The field is uniform and perpendicular to one side of the conductor. The derivation is based on a numerical solution of the problem, using the finite-difference technique of successive over-relaxation.