An integral for self inductance of thin wires

Abstract I propose an elegant method of calculating the self inductance of a thin wire of arbitrary shape. The inductance is broken to into two parts - the inductance of a straight wire of the same length and cross section, and the remainder, the ‘curve inductance’ due to the shape of the axial curve. The curve inductance is finite and can be calculated from a double integral by subtracting the straight wire singularity inside the integrand. Unlike all other methods, this does not involve a small parameter, and can be applied to any curve knowing its arc length parameterization. We use the circular arc and helix as examples and find that the integral is fast and accurate. The limits of the approximation are investigated for touching parallel wires.