Eddy current damping revisited

We consider energy loss from eddy currents on intermediate length scales not previously considered. We find the exact solution for the eddy currents evoked by an oscillatory flux in a thread along the axis of a conducting cylinder. When the radius of the thread is small compared to the skin depth, the eddy currents are concentrated in the vicinity, shielding the matrix from the internal disturbance, and the power loss has a dominant term that increases logarithmically as the radius vector to the center decreases. An array of parallel threads can be treated as a model for a heterogeneous distribution of magnetization, either in a single material partially magnetized or a material of more than one phase, of which at least one is ferromagnetic.