The thesis discusses the skin and proximity effects, which are important physical phenomena in the theory of electromagnetism. The skin effect describes the tendency of alternating current to concentrate primarily at the surface of a conductor due to the induced magnetic field. The near-field phenomenon occurs when there are multiple conductors in the space. In this case, the magnetic field of the current in one conductor affects the distribution of the current in the other conductor, resulting in additional irregularities in the distribution of the current. Both phenomena significantly reduce the effective cross-sectional area or increase the resistance of conductors and the associated losses, so they must be considered when designing electrical devices and systems, especially at higher frequencies.
For better understanding and illustration of these two phenomena, we developed a numerical model in the Wolfram Mathematica software environment, which enables visualization of the distribution of current density and magnetic field. In the model, we considered two parallel copper conductors with a square cross-section, through which current flows in opposite directions. We calculated the values of penetration depth at different frequencies and displayed the current density distributions at different frequencies and distances between the conductors. We also calculated the alternating resistance and compared it to the direct resistance. As the frequency increases, the alternating resistance increases until it reaches the saturation point, when the electric current flows exclusively along the conductor's circumference. At the end, we drew the magnetic field vectors around the conductors.
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