EM Tracker HFluxPerI Derivation

6DOF electromagnetic tracker electromagnetics

All of the following can be found in classical-electromagnetics textbooks.

We assume that, at the working frequency or frequencies, the wavelength is large compared to the distance between transmitter coil trio and receiver coil trio. This is the quasi-static approximation, which permits us to ignore radiation fields.

We assume that each coil is so small that its shape does not matter, only its size times its number of turns. This is the dipole approximation. Each coil has an effective-area vector, Aeff_vector (usually measured in square meters) which completely describes a dipole coil's quasi-static magnetic properties.

Consider a single transmitter coil, with effective-area vector Aeff_transmitter_vector. We pass a current I (usually measured in amperes) through the transmitter coil, which causes the coil to emit a vector magnetic field Hvector which varies depending upon where we observe the magnetic field.

Let Rvector (usually measured in meters) be the vector from the transmitter coil to the position of the magnetic-field observer. The magnetic field at the observation point is Hvector(Rvector).

We can write Rvector as the product of its scalar magnitude, Rmagnitude, and a unit vector Runit_vector in the direction of Rvector:

Rvector = Rmagnitude * Runit_vector