Solid rectangular and T-shaped conductors in semi-closed slots

Summary Previous methods of calculating the internal impedance of rectangular and T-shaped conductors have made arbitrary assumptions about the form of the magnetic field. These have led to inconsistencies. A method is developed which necessitates less restrictive assumptions, thereby removing the inconsistencies. Results are compared for typical conductor sizes.List of symbols a, b, c, d dimensions of conductor or slot - J current density - E electric field strength - V scalar potential - I current (r.m.s.) in conductor - B flux density - H magnetic field strength with componentsH _x,H _y in thex, y coordinate directions respectively - L inductance/unit length - R resistance/unit length - A vector potential - A modified vector potential - A ^*,A ^** single and double cosine transforms ofA - conductivity of conductor - relative permeability of conductor - angular frequency - ² j ₀ - m, n transform parameters - C _m {(m/c)²+ ₁ ² }^1/2 - D _n {(n/d)²+ ₂ ² }^1/2 - P _m,Q _n coefficients - K constant of integration - Re, Im real imaginary parts of complex function respectively