A study of the lines of flow and the equipotential lines in a plate conductor

Abstract

The function z = w + k√(w² - 1) will represent in the z plane the lines of flow of an electric current in a plate conductor around a circle of unit radius if the constant k is unity and around an ellipse of the form x²/1 + y²/k² = 1 which is oblate if the constant k is greater than unity and prolate if the constant k is less than unity.

The lines of flow of an electric current approach straight lines in the z plane as y increases and the smaller the vertical axis of the deleted section the smaller will be the distortion of the lines of flow.

The finding of the lines of flow of an electric current in a plate conductor around a square section does not admit of a mathematical solution.

The magnetic lines in a field which has been partially blocked out do not conform to "bending" as do the lines of flow of an electric current in a plate conductor in which sections of certain families of geometric figures have been deleted.

Lines of flow in a plate conductor with certain deleted geometric sections do conform with the theoretical lines mathematically calculated and plotted when the conductor is placed in the magnetic field.