Speed of Magnetic Field Propagation in a Conductor

When a voltage source is connected to a long conductor, the magnetic field propagates along the conductor at a speed close to the speed of light in vacuum (about 85% of the speed of light), but the direction of propagation depends on how the electric current is established. In an ideal case when connecting a voltage source, the magnetic field appears simultaneously along the entire length of the conductor, since the change in the electromagnetic field propagates as a wave, not as separate particles.

Contents

• Physics of Magnetic Field in Conductors
• Propagation Speed of Magnetic Field
• Behavior in Long Conductors
• Propagation in an Open Ring
• Experimental Evidence
• Practical Implications

Physics of Magnetic Field in Conductors

The magnetic field around a current-carrying conductor arises according to Ampere’s law and follows the right-hand rule. When current flows through a conductor, the magnetic field has cylindrical symmetry and is directed azimuthally around the conductor. As explained in electronic textbooks, the magnetic field lines form closed concentric circles around the conductor.

It is important to understand that the magnetic field is a byproduct of charge movement, not their direct transport. Electrons in the conductor move at very low speeds (drift) - about millimeters per second, while the electromagnetic field itself propagates at a much higher speed.

Propagation Speed of Magnetic Field

The propagation speed of the electromagnetic field in a conductor is significantly higher than the speed of electrons. According to research, electromagnetic waves in conductors propagate at a speed of approximately 85% of the speed of light [source]. This means that when connecting a voltage source, the change in the electromagnetic field will reach any point in the conductor almost instantaneously from a human perception standpoint.

In contrast, the speed of “electricity” as such in conductors can be much lower. For good conductors, the propagation speed of the electric field can be as low as about 3.2 m/s as a consequence of Snell’s law and the extremely low speed in conductors [source].

Behavior in Long Conductors

When connecting a voltage source to a long conductor, several phases of field propagation can be distinguished:

1. Initial phase (first nanoseconds): Appearance of the electromagnetic wave from the voltage source
2. Current establishment: Gradual increase of current to steady-state value
3. Steady state: Constant magnetic field around the conductor

As noted in physics forums, there is a difference between the propagation of the electromagnetic field around the conductor (about 85% of the speed of light) and the calculated speed of electrons in the conductor, which is significantly lower.

Propagation in an Open Ring

In the case of a very long conductor in the form of an open ring (for example, around the Earth) when connecting a voltage source:

• The magnetic field does not appear instantaneously along the entire length, but propagates as an electromagnetic wave
• The wave begins to propagate from the point where the voltage source is connected
• The propagation speed is approximately 85% of the speed of light
• If there are magnetic field sensors along the conductor, they will detect the appearance of the field in a sequence corresponding to the wave propagation

For a conductor comparable in length to the size of the Earth (about 40,000 km), the propagation time of the electromagnetic wave would be approximately:

$$t = \frac{d}{v} = \frac{40,000,000 \text{ m}}{0.85 \times 3 \times 10^8 \text{ m/s}} \approx 0.16 \text{ seconds}$$

This means that in an ideal case without propagation delays along the entire length of the conductor, the magnetic field will be established in approximately 0.16 seconds.

Experimental Evidence

Experimental research shows that changes in the electromagnetic field do indeed propagate at a finite speed. According to Physics Stack Exchange, the electric field in a conductor is residual (strong enough only for electrons to overcome the resistance of the conductor), while useful energy propagates outside the wire in the form of a rotating magnetic field.

The correct mechanics of this process use Liénard-Wiechert potentials, which take into account causality and the finite speed of light in classical electromagnetic theory [source].

Practical Implications

For practical applications, it is important to understand:

1. Synchronization: In very long systems, a noticeable propagation delay of the field may occur
2. Wave effects: With rapid voltage changes, reflections and wave interference may occur
3. Distributed parameters: In long conductors, it is necessary to consider distributed inductance and capacitance

For most engineering applications in practice, the propagation of the magnetic field is considered practically instantaneous, as the speed of light is very high compared to the size of typical systems.

Conclusion

1. The magnetic field along a long conductor propagates at a speed close to the speed of light (about 85% c), not instantaneously
2. In the case of an open ring around the Earth, the field will propagate from the point where the voltage source is connected in approximately 0.16 seconds
3. The direction of propagation is from the voltage source along the conductor, not from negative to positive or vice versa
4. The magnetic field does not arise “simultaneously along the entire length” in the strict physical sense, but propagates as an electromagnetic wave
5. For most practical purposes, this propagation can be considered practically instantaneous due to the high speed of light

Thus, when connecting a voltage source to a long conductor, magnetic field sensors will detect the appearance of the field in a sequence corresponding to the propagation of the electromagnetic wave from the connection point, not instantaneously along the entire length.

Sources

1. Speed of electricity - Wikipedia
2. Electromagnetic Waves speed in Conductor - Physics Forums
3. What are the fields produced around a current carrying conductor? - Physics Stack Exchange
4. Intro to Magnetic Fields Around a Conductor and a Coil - EEPower
5. Electromagnetism and Electricity for Electromagnets - Electronics Tutorials
6. Magnetic Fields Produced by Currents: Ampere’s Law - Douglas College
7. Has the speed of propagation of a magnetic force field been measured? - PhysLink