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Mathematical model of a solenoid for energy and force calculations

The radial and axial forces on a solenoid are found with a new technique. The authors represent a solenoid by many circular filaments and the self inductance of each filament and the mutual inductances between each two filaments are calculated using Grover's tables. Then the energy is calculated by summing the mutual plus self inductive energies. The radial force is calculated by using the principle of virtual work in which an increase of one of the radii ri, by dri changes the energy with respect to this change in r. The axial forces are calculated by the same technique, that is by increasing one of the axial distances zi by dzi and calculating the change in energy with respect to this change in z.