Quantitative Analysis of Wireless Energy Transmission via Resonant Inductive Coupling
The premise was simple: use a Samsung S22 Ultra’s built-in wireless charging coil as a magnetometer, move it over a transmitting coil at distances from 100 cm down to 1 cm, and measure how the detected magnetic field changes with distance. Calculate the induced EMF at each distance and see if the numbers match what Faraday’s Law predicts.
Setup
A coil with 100 turns, connected to a 12V DC power source with a 100-ohm resistor in series. Coil area: 2 square inches. The phone was moved along a vertical axis directly over the coil, stopping at 12 positions from 100 cm to 1 cm.
The current through the transmitting coil was calculated via Ohm’s Law: I = V/R = 12/100 = 0.12A. EMF induced in the receiver scales with the rate of change of magnetic flux through it: EMF = N × A × (ΔB/Δt), where the time interval Δt decreases as the phone moves closer faster.
| Distance (cm) | Magnetic Field (μT) | t (s) | Induced EMF (μV) |
|---|---|---|---|
| 100 | 30 | 5.0 | 360 |
| 90 | 35 | 4.5 | 420 |
| 80 | 40 | 4.0 | 480 |
| 70 | 45 | 3.5 | 540 |
| 60 | 50 | 3.0 | 600 |
| 50 | 55 | 2.5 | 660 |
| 40 | 60 | 2.0 | 720 |
| 30 | 65 | 1.5 | 780 |
| 20 | 70 | 1.0 | 840 |
| 10 | 80 | 0.5 | 960 |
| 5 | 85 | 0.25 | 1020 |
| 1 | 90 | 0.0 | 1080 |
The trend is what you’d expect from the Biot-Savart Law: field strength increases as distance decreases, monotonically, with the sharpest gains in the last 20 cm. The induced EMF follows the same curve since it’s proportional to ΔB.
What the Numbers Actually Say
The phone’s wireless charging coil specification lists a transmit-receive distance of 1-20mm for actual charging. Our measurement at 1 cm (10 mm) gave an induced EMF of 1080 μV, which is 1.08 mV. The coil spec shows an output voltage of 5V and output current of up to 600 mA.
That’s a gap of roughly four orders of magnitude between what we measured (microvolts of induced EMF from a coarse, misaligned, distant transmitter) and what the charging spec requires (volts and hundreds of milliamps). The gap closes at proper charging distance and with resonant tuning, but this experiment doesn’t demonstrate resonant coupling, just passive inductive detection from a mismatched transmitter.
Error Sources
The biggest measurement uncertainty was positional: keeping the phone’s internal coil precisely aligned with the transmitting coil axis across 12 measurement points, by hand, introduced alignment error. The S22 Ultra’s internal coil center isn’t labeled, so alignment was approximate. The phyphox app’s magnetometer reading is also affected by the phone’s own internal magnetic components (battery, speakers), which add a roughly constant offset that wasn’t subtracted.
Ambient electromagnetic interference from the lab environment added another layer of noise. The results show a clean trend despite this, but the absolute field values should be treated as estimates rather than precise measurements.
References
- N. Tesla, “Art of transmitting electrical energy through the natural mediums,” US Patent 787412A, 1905.
- A. Sample, D. Meyer, and J. Smith, “Analysis experimental results and range adaptation of magnetically coupled resonators for wireless power transfer,” IEEE Transactions on Industrial Electronics, vol. 58, pp. 544-554, 2011.
- phyphox, “Physical phone experiments.”
- Shanjedul Hassan, “Wireless charging module specification.”