On eddy currents in a rotating disk

A DEVICE which often occurs in electric machines and instruments consists of a relatively thin conducting disk rotating between the pole pieces of a permanent magnet or electromagnet. The author has received inquiries as to the method of calculating the paths of the eddy currents and the torque in such cases. The following rather simple method, which is quite accurate for a permanent magnet, seems not to be described in the literature. It assumes that the disk is so thin that the skin effect can be neglected. This is true for all frequencies that can be produced mechanically. To facilitate calculation in the special case of circular poles it is also assumed that 2πωabγ=εa is much less than one where ω is the angular frequency of rotation in radians per second, a the pole-piece radius, b the disk thickness, and γ the electric conductivity, all in centimeter-gram-second electromagnetic units. This produces a fractional error of less than εa in the eddy current densities and of less than (εa)
²
in the torque. In the case of the electromagnet the situation is complicated by the presence of the permeable pole pieces in the magnetic field of the eddy currents. This may send a large demagnetizing flux through the electromagnet. An approximate solution for this case will be considered.