Electromagnetic Fields in Wireless Power Transmission
Wireless power transmission makes use of a pair of magnetically coupled coils, each in series with a capacitor. The characteristic frequency is discussed in the companion Demonstration "Wireless Power Transmission." The present Demonstration is concerned with the electromagnetic fields associated with a wireless transmission system. The parameters are the following (as defined in the companion Demonstration):[more]
, , ,
, (corresponding to , , , )
Maximum power is transmitted at the resonance frequency .
The instantaneous input voltage and currents , can be defined from the corresponding phaser solution of the circuit equation. The field of the coaxial coil system can be readily analyzed using the vector potential , which is a linear function of and . Assuming a near field, the electric and magnetic fields can be obtained by and , respectively. The power flow through space is given by the Poynting vector .
The field in the - plane is shown for a selected frequency and phase (i.e., time). The electric field perpendicular to the - plane is not shown. The magnetic field and Poynting vectors are shown by blue and orange arrows, respectively. The color indicates the magnitude of the energy density . All of these are plotted on a logarithmic scale.[less]
In the case of resonance (Snapshots 1 or 2), substantial power emanates from the coils due to the enhanced currents. Notice that the power flows to coil 2 even at the instant (Snapshot 2). The energy and power level are constrained in the off-resonance condition, as seen in Snapshot 3.
 J. Garnica, R. A. Chinga, and J. Lin, "Wireless Power Transmission: From Far Field to Near Field," Proceedings of the IEEE, 101(6), 2013 pp. 1321–1331. doi:10.1109/JPROC.2013.2251411.
 J. D. Jackson, Classical Electrodynamics, 3rd ed., Hoboken, NJ: John Wiley, 1998.