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