Estimating Calculation of the Displacement Current Density and Its Influence on Electromagnetic Processes in a Metallic Conductor with Alternating Conduction Current

The paper presents the results of an approximate calculation of the density δ_s(t) of displacement current i_s(t) and an assessment of the influence of the density on electromagnetic processes in an isotropic nonmagnetic metal (alloy) of a continuous cylindrical conductor of finite dimensions (radius r₀ and length l₀ \( \gg \) r₀) with an electric alternating (pulsed) axial conduction current i₀(t) with various amplitude–time parameters. The obtained theoretical data on the quantized (discrete) spatiotemporal distributions of standing longitudinal waves (half-waves) of density δ_s(t) of displacement current i_s(t) in this conductor allow one to conclude that electrodynamic calculations of variable (pulsed) electromagnetic processes occurring both in the conductor and in the electric circuit connected to it can ignore the influence of the longitudinal waves (half-waves) of density δ_s(t) of displacement current i_s(t) and the displacement current i_s(t) itself in the conductor, and these quantities in practical field calculations can be neglected. It was determined that the waves (half-waves) of density δ_s(t) of displacement current i_s(t) and the displacement current i_s(t) itself preserve the solenoidality (closeness) of the total electric current i_i(t) = i₀(t) + i_s(t) in the conductor and its circuit. It was shown by calculation that the displacement current i_s(t) and its density δ_s(t) in the nonmagnetic metal (alloy) of the conductor do not suffer thermal (Joule) energy losses.