Analysis of a Nonlinear Electromagnetic Field Penetration Problem,
CONSTRUCTION ENGINEERING RESEARCH LAB (ARMY) CHAMPAIGN ILL
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This study examines the time-dependent penetration of a step increase in magnetic field strength H into a semi-infinite conducting medium having a permeability which varies with magnetic field strength. The medium is considered to be isotropic, homogeneous, and initially demagnetized. The medium at any point is presumed to follow its initial magnetization curve for which a simple approximation is assumed. The analytical approach consists of mathematical analysis supplemented with numerical calculations. The problem can be simplified from one involving a second order nonlinear partial differential equation to one involving a second order nonlinear ordinary differential equation utilizing a simple transformation of variables. Although a formal parametric representation of the solution of the second order differential equation is considered, a simple closed form solution in terms of elementary functions does not seem to exist. Hence several analytical techniques, as well as numerical calculations, have been employed to deduce properties of the solution.
- Numerical Mathematics
- Electricity and Magnetism