## Mathematics Faculty Publications

#### Title

Symbolic Computation with Maple for Eddy Current Response to Variation in Surface Conductivity with Depth

Presentation

7-2004

#### Abstract

An Eddy current is the current induced in little swirls("eddies") on a large conductor. If a large conductive metal plate is moved through a magnetic field that is perpendicularly to the sheet, the magnetic field will induce small "rings" of current which will actually create internal magnetic fields opposing the change. Eddy current can be either good or bad things depending on applications. We need to prevent AC energy from being lost to eddies generated within the magnetic core. On the other hand, Eddy currents help turn kinetic energy quickly into other forms of energy. Because of this, braking systems have been created that take advantage of it. Adding a magnetic field around a spinning piece of metal will cause eddy currents in that metal to create magnetic fields that will quickly slow down the spinning object, as long as the magnetic field is strong enough. Eddy current inspection can be used to detect seams, laps, cracks, voids, and inclusions. A number of factors, apart from flaws, will affect the eddy current response from a probe, including material conductivity, permeability, frequency, and proximity. Successful assessment of flaws or any of these factors relies on holding the others constant, or somehow eliminating their effect on the results. It is this elimination of undesired response that forms the basis of much of the technology of eddy current inspection. The purpose of this presentation is to show how the computer algebraic system Maple can be used effectively in studying a model problem of eddy current response to variation in surface conductivity with depth.

#### Original Citation

Shao. S. (2004). Symbolic Computation with Maple for Eddy Current Response to Variation in Surface Conductivity with Depth. Maple Summer Workshop, July 11 - 14, 2004, Wilfrid Laurier University, Waterloo, Ontario, Canada, p. 1-21.

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