Skin effect in rectangular conductors at high frequencies

There is at present little exact information either theoretical or experimental on the high frequency resistance of cylindrical conductors of rectangular section, although the general nature of the phenomenon is quite well known and has been exhaustively treated in the case of circular conductors by Kelvin, Heaviside, Russell and others. The first method of attack on the problem of the rectangular conductor is to treat it as a strip of infinite breadth when the problem becomes one dimensional and requires simply a solution of ∂2 E/∂x 2 = 4πμ/ρ ∂E/∂t E being the electrical force and μ and ρ the permeability and resistivity respectively. The solution of the problem for two parallel strips was first given by Rayleigh and it was shown that for high frequencies the current decreases exponentially toward the centre of the conductor, being confined effectively to a surface layer so that the resistance of the conductor was the same as if composed of surface strips of thickness (2πμω/ρ)-½ , ω to being the periodicity. This approximation, however, gives much too low values for the high frequency resistance of a conductor of finite breadth.