Field gradient analysis of a conical helix (for EM levitation melting)

The excitation coil used in electromagnetic-levitation melting consists of a few turns of copper tubing wound over a length of a few centimeters. The behavior of the field and the Lorentz force on a conducting specimen in it are studied for a typical coil. The equations for the field and field gradient for this excitation coil are obtained by modeling it as a helix wound over the surface of a cone. Results for the field and the Lorentz force on a conducting specimen due to current flowing in a right circular helix are presented. These results are compared with the results for an equivalent stack of coaxial loops for a typical laboratory coil. It is shown that the helix model is more realistic than the 'stack of coaxial loops' model. In the limit of vanishing pitch of the coil, the helix and the stack models are shown to be equivalent.< >