## 1952a

The following is a paper by H. Aspden published in the Journal of Applied
Physics, vol. 23, pp. 523-528 (1951).

### EDDY-CURRENTS IN SOLID CYLINDRICAL CORES HAVING NON-UNIFORM
PERMEABILITY

**Abstract**: A method of estimating magnetization
losses in solid cylindrical cores of ferromagnetic material is given. The
conception of complex permeability is introduced to show the effects which
hysteresis has upon the degree of flux penetration. A formula is given for the
effective permeability which should be used in the classical treatment in which
non-linearities have been ignored. An arbitrary case in which the permeability
changes across the core section is considered and the solution is extended to a
core which is homogeneous, but whose permeability changes with the degree of
magnetization. In this way errors due to a non-linear B-H curve are reduced and
the complex permeability notation is shown to lead to a more reasonable
Steinmetz relationship. The eddy-current anomaly is mentioned and it is noted
that the theory developed is suited to a consideration of the anomaly as
explained in terms of time-lag effects.

**Commentary**: This paper was
written during a period when the author was working for a Ph.D. degree which
involved experimental research on the eddy-current anomaly. See the related
paper: [1956a].
However, the detailed analysis based on complex magnetic permeability as covered
by the mathematics in this paper in relation to a non-linear B-H magnetization
curve was not included nor involved in the research thesis which was submitted
in support of that Ph.D. degree.