Uniform magnetic field coils construction optimization

Optimization of uniform magnetic field generation through the variation of magnetic coil sizes and positions is derived through calculation of the magnetic field of ideal circular coils for Helmholtz and Maxwell coils, achieving at least 20% increase of uniform field area. Analytical solution for Biot-Savart law for circular current loop is used to perform all computational results. Sensitivity to dimensional imperfections is given and it is also shown that multi-turn coils have negligible effect on the generated field as long as coil cross-section dimensions are small compared to coil radius. The reference calculation results are compared by experimental measurements.