A changing magnetic field from the transmitter coil (left) induces
a current in the receiver coil (right) — Faraday's law, V = -N·dΦ/dt.
Transfer is strongest when both coils resonate at the same frequency
(detune = 0%) and weakens quickly with distance. Drag to orbit the scene.
The coupling coefficient falls off steeply with separation d, roughly
as the near-field dipole scaling used here for the mutual inductance M:
κ(d) ∝ 1 / d³
M = κ·√(L₁·L₂)
P_load = κ · V² · 4·R_s·R_L / (R_L + R_s)²
η = κ · R_L / (R_L + R_s)
- Coil distance — sets the separation d; coupling κ collapses roughly with 1/d³, so power fades fast as the coils move apart.
- Detune from resonance — mismatches the transmitter/receiver resonant frequency; even with coils close together, transfer drops off a resonance peak just like a driven RLC circuit.
- Load resistance — the receiver's electrical load R_L. Power delivered peaks when R_L matches the source/coil resistance R_s (maximum power transfer theorem), while efficiency keeps climbing as R_L increases — a classic power-vs-efficiency trade-off.
This is the same physics behind Qi wireless phone charging and inductive EV
charging pads — both tune resonant frequency and coil alignment to maximise κ,
then choose a load impedance that balances delivered power against efficiency.