Empirical expression for the axial field of cylindrical bar magnets

Theoretical values of the magnetic field intensity outside a permanent magnet usually agree with experiment only at distance greater than the length of the magnet. This theoretical formula is modified to fit experimental results at shorter distances as well so that it can serve as a convenient analytical approximation for practical problems involving cylindrical bar magnets. Measurements are reported for the field of five Alnico V magnets whose diameters are roughly 1/8,3/16,1/4,1/2, and 1 inch, and whose lengths range from 4 to 6 inches. For all these, the modified formula describes the axial field in a distance range of 9 to 81 mm from the nearest face of the magnet to within a few percent from the measured values.