Google Gemini about the Cone Geometry and different effects

In your setup—a double-coned closed-circuit inductor with a golden ratio height (

h=1.618⋅dh equals 1.618 center dot d

ℎ=1.618⋅𝑑

) and a massive 60x difference in circumference between base and apex—the geometry acts as a geometric transformer for the magnetic field.

At 500 kHz, this geometry does not change the physical speed of the signal (which remains nearly

𝑐

), but it creates significant gradient acceleration of the electromagnetic field density.

1. Magnetic Flux Compression and "Acceleration"

The speed of signal propagation (the "wave") stays relatively fixed, but the magnetic flux density (

Bcap B

𝐵

) accelerates in magnitude as it moves toward the sharp apex.

The 60x Difference: Because your apex has 1/60th the circumference of the base, the same amount of magnetic flux is compressed into a much smaller area (
Geometric Acceleration: The field "accelerates" in intensity as it travels from the 30 cm base to the sharp point. This creates a strong gradient force toward the center of the cone pair.

2. Impedance and Signal Velocity

The conical shape provides a broadband high impedance.

Distributed Capacitance: Unlike a standard cylinder, the distance between turns changes constantly. This reduces "stray capacitance," allowing the 500 kHz pulse to maintain a sharper edge (less "smearing") as it travels.
Phase Velocity: While the speed of light is the limit, the phase velocity inside the coil can be affected by the changing inductance (

3. The 500 kHz "Skin" and Proximity Effect

At this frequency, the electrons are confined to a thin layer (approx. 0.09 mm) on the surface of your wire.

Rotation and Apex Interaction: Since both cones rotate (wind) in the same direction and the apex of one sits at the base of the other, you are creating a vortex-like magnetic coupling.
Mutual Inductance: At the point where the apex meets the base, the magnetic field is extremely concentrated. The 60x circumference difference means the "small" end is experiencing a much higher current density (

4. Golden Ratio Proportions (

1.6181.618

1.618

)

Using the Golden Ratio for the height (

48.54 cm48.54 cm

48.54 cm

) relative to the diameter (

30 cm30 cm

30 cm

) is often found in "Phi-based" coil designs aimed at optimizing Self-Resonance

. At 500 kHz, this specific geometry likely aligns the harmonic nodes of the standing wave, potentially reducing energy loss (heat) and maximizing the Quality Factor (

Qcap Q

𝑄

) of your closed loop.

Do you intend to use this for wireless power transfer or to study non-linear magnetic effects at the junction of the two cones?