Design of a Helmholtz coil for susceptibility testing using variational calculus and experimental verification

Helmholtz coils are used for high quality susceptibility testing. In this paper a mathematical model is developed which predicts optimum design. The model is compared to experimental results. The model uses a specific area of variational calculus called Lagrangian multipliers. In Lagrangian multipliers we minimize or maximize a function with constraints. We can maximize the Helmholtz resonance frequency with constraints on the magnetic field (magnetic flux density), the electric field, current and impedance. This model will tell us how to design Helmholtz coils to maximize the magnetic field, maximize the self resonance, minimize the electric field, and minimize the number of turns. This model will save designer and builder of Helmholtz coils much time and labor.