Edge effect for transverse electromagnetic field penetration into a conductor

Abstract

The magnetic field absolute value |H| calculated within the ideal conductivity approximation is known to behave near the conductor edge according to the law |H| = C S^α Here s is the shortest distance between a given point and the conductor edge, which is a dihedral angle θ <; π. The factor C is determined by the magnetic system configuration and by currents in the conductors. The coefficient α = (θ - π)/(2π - θ), therefore |H| grows unrestrictedly at S→0. For a medium with a finite conductivity, a formula derived in the linear approximation, which gives a possibility to calculate the magnetic field near the dihedral angle edge (in the point S = 0), when the skin depth is small. This formula reads H(0) = γC Δ^α for the sinusoidal current. Here Δ is the skin depth, γ is the frequency-independent dimensionless factor. Factor γ(π/2) is calculated. Formulae for the current density in the angle θ apex, for the Joule heating and for the volume energy density in this point are derived.