Predicting the magnetic field from twisted three-phase arrangement

The low-frequency magnetic field in the vicinity of a twisted three-conductor arrangement carrying balanced three-phase current is studied by analytical methods. Formulae are derived for the field vector as function of observation point location, with pitch and radius of the helix as parameters. Exact analytical expressions are given for the field as function of time as well as for the effective value of the field components and the total field in form of Bessel-function series. The field vector is expressed in helical coordinates. Approximations for the field far away from the arrangement are given. Verifying measurements have been performed on a rig.