Calculation of Magnetic Stiffness over Torque between Two Current-Carrying Circular Filaments Arbitrarily Positioning in the Space

The sets of expressions for calculation of sixteen components of magnetic stiffness over torque between two current-carrying circular filaments arbitrarily positioning in the space are derived by using mutual inductance and Grover’s method. The expressions are presented in the analytical form via integral equations, whose kernels include the elliptic functions of first and second kinds. The derived sets of formulas were mutually validated and results of calculation of components of magnetic stiffness agree well to each other.