From: veritasium
A common thought experiment involving a gigantic circuit with light-second long wires connecting to a light bulb just one meter from the battery and switch initially posited that the light bulb would illuminate in 1/c seconds after the switch closed [00:00:00]. This claim sparked significant debate and was deemed “wrong,” “misleading,” and a violation of causality by many [00:00:20]. The controversy highlighted the need to clarify fundamental concepts of how electricity works in circuits, moving beyond simplified models to the underlying physics governed by Maxwell’s equations [00:00:38].
To address the confusion, a scaled-down model circuit, 10 meters in length on either side, was built at Caltech to observe phenomena within the first 30 nanoseconds using fast scopes [00:00:47]. This setup aimed to measure the time delay and magnitude of voltage across a resistor (standing in for a light bulb) after a pulse was applied [00:01:15]. The key claim was that a visible amount of power, significantly greater than leakage current, would be present at the load in roughly the time it takes light to cross the one-meter gap between the switch and the bulb [00:02:09].
Misconceptions About Electricity in Circuits
Several common misconceptions about electricity in circuits need to be addressed to understand circuit dynamics fully:
Misconception 1: Electrons Carry Energy from Battery to Bulb
Many believe that electrons carry energy from the battery to the bulb, dissipating their kinetic energy as heat [03:31:00]. However, an electron often hasn’t been near the battery if the circuit has only been on for a short time [03:49:00]. Electrons gain kinetic energy from an electric field in the wire, which is then transferred to the lattice through collisions, causing heating and light emission [03:57:00]. Therefore, while electrons transfer energy to the lattice, the energy itself originates from the electric field [04:11:00].
Misconception 2: Mobile Electrons Push Each Other
Another misconception is that mobile electrons push each other through the circuit via mutual repulsion, similar to water in a hose or marbles in a tube [04:30:00]. In a conductor, the negative charge of electrons and the positive cores of atoms perfectly cancel out on average, resulting in zero charge density inside [04:45:00]. For every repulsive force between electrons, there’s an equal and opposite force from the positive ion nearby, meaning mobile electrons cannot push each other along the wire [04:57:00].
Misconception 3: Electric Field Comes Entirely from the Battery
It is intuitively thought that the electric field driving the circuit comes entirely from the battery, being the active element [05:13:00]. However, if this were true, a light bulb would glow much brighter when placed closer to the battery, which it doesn’t [05:31:00]. The truth is that the electric field in the wire is generated by both the battery and charges on the surface of the wires [05:45:00].
The Role of Electric Fields and Surface Charges
The true understanding of circuit behavior lies in the interactions of electric fields and surface charges:
- Along the wire, from the negative to the positive end of the battery, a gradient of charge builds up on the wire’s surface [05:54:00]. This includes an excess of electrons near the negative terminal and a deficiency (exposed positive cores) near the positive terminal [06:01:00].
- These surface charges, along with the charges on the battery, create the electric field both inside and outside the wires [06:18:00].
- These surface charges are established almost instantaneously when the battery is connected, limited only by the speed of light [06:29:00]. Even a slight expansion or contraction of the electron sea by the radius of a proton is enough to establish these charges [06:42:00].
- The battery continuously works to maintain this surface charge distribution [07:02:00].
- In a load (like a resistor), the electric field generated by these surface charges accelerates electrons, which then dissipate their energy through collisions with the lattice [07:12:00].
- This means the battery puts energy into the field, and electrons then extract that energy from the field and transfer it to the load [07:21:00].
- An analogy describes the battery as a shepherd, surface charges as sheepdogs responding to orders, and mobile electrons as sheep guided by the dogs [07:33:00].
A VPython simulation shows how the entire charge distribution creates a net electric field, depicted by orange arrows, everywhere in and around the circuit [07:55:00]. The steepest gradient of surface charges, and thus the largest electric field, occurs in the resistor due to its narrower cross-section requiring a higher electron drift velocity to maintain current [08:49:00]. Far from the battery, most of the electric field is due to surface charges [09:06:00].
Circuit Dynamics and Causality
When a battery is connected to a circuit, even with an open switch, charges rearrange themselves on the surface of the wires and switch until the electric field inside the conductor is zero [10:17:00]. The full potential difference of the battery is then across the switch [10:53:00].
When the switch is closed:
- Surface charges on both sides neutralize instantly on contact [11:02:00].
- At that instant, the electric field inside the conductor is no longer zero, and current begins to flow through the switch [11:08:00].
- Simultaneously, the new electric field, stemming from the modified surface charges, radiates outwards at the speed of light [11:17:00].
- When this radiating electric field reaches the bulb, the electric field inside it becomes non-zero, and current starts to flow there as well [11:24:00].
This explains why the bulb lights up in roughly the time it takes light to cross the one-meter gap between the switch and the bulb (one meter divided by c) [11:32:00].
Causality and Disconnected Wires
The initial lighting of the bulb does not violate causality, even if parts of the circuit are half a light-second away [12:51:00]. This is because the current flows through the load due to the local electric field it experiences [13:24:00]. Simulations show that the response of a completely disconnected wire to the changing electric field is virtually identical to that of a connected wire, at least until the signal reflects back from the far end [13:31:00]. This means the initial current flow at the bulb is independent of the circuit’s completeness further away.
Energy Flow via the Poynting Vector
The Poynting vector, which is the cross product of electric and magnetic fields, indicates the direction of energy flow [13:54:00]. After the switch closes, the Poynting vector points out of the battery and straight across the gap to the other wire, regardless of whether it’s connected [14:04:00]. This demonstrates that energy is carried by the fields, not by electrons, and can thus travel directly across space [14:12:00].
While wires are not strictly necessary for power transfer (e.g., wireless charging [14:22:00]), they are more efficient because they channel the fields and, consequently, the energy from the source to the load [14:33:00]. The Poynting vector also shows energy being carried outside the wires, not within them [14:55:00].
Circuit Models: Lumped vs. Distributed Elements
Analyzing circuits using direct solutions to Maxwell’s equations in three dimensions is complex [15:01:00]. To simplify, scientists and engineers use models:
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Lumped Element Model: This is the common approach where complex multi-particle and field interactions are simplified into discrete circuit elements like resistors, capacitors, and inductors [15:35:00]. Ohm’s law (V=IR) is a macroscopic result of these underlying field interactions [15:14:00]. Standard circuit diagrams rely on this model. However, for the ‘gigantic circuit’ problem, this model is flawed because it doesn’t account for the important fields between the wires [15:48:00].
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Distributed Element Model (Transmission Line): For long wires where inter-wire fields are significant, this model is necessary. It involves adding distributed capacitors along the wires (capturing the effect of charges on one wire influencing the other) and inductors (modeling the magnetic fields that resist current changes) [16:00:00]. For superconducting wires, it would primarily consist of distributed capacitors and inductors [16:34:00]. This model helps explain immediate current flow: when voltage is applied, current flows as capacitors charge sequentially, creating an expanding loop of current at nearly the speed of light [16:49:00].
The distributed element model allows for calculating the characteristic impedance of transmission lines (the resistance to alternating current a source would see) using the square root of inductance divided by capacitance [17:23:00]. For the experimental circuit, the measured characteristic impedance was about 550 Ohms, leading to the selection of a 1.1 kilo-Ohm resistor for maximum power transfer [17:45:00].
Experimental Validation and Conclusion
A scaled-down experiment demonstrated that after a few nanoseconds, the voltage across the resistor rose to about 4 volts [18:59:00]. With a 1 kilo-Ohm resistor, this meant 4 milliamps of current were flowing, transferring about 14 milliwatts of power before the signal traversed the entire circuit [19:04:00]. This amount of power is sufficient to produce visible light if routed through an appropriate device like an LED, which was demonstrated [19:16:00]. This was significantly more power than would be attributed to simple leakage current [19:22:00].
Further simulations by Ben Watson using Ansys HFSS, a software that provides complete solutions to Maxwell’s equations in 3D, confirmed these results [12:01:00]. Other YouTubers, such as Alpha Phoenix and ZY, also independently verified similar outcomes with their own experiments and simulations [20:22:00].
Ultimately, this thought experiment serves to illustrate a fundamental aspect of electricity often obscured by simplified teaching methods: the main actors in a circuit are the electromagnetic fields, not the electrons themselves [21:05:00]. The fields carry the energy, and the electrons are guided by them [10:07:00]. This perspective is crucial for understanding high-speed circuits and transmission lines, where traditional voltage and current models can be insufficient [21:13:00]. As veteran printed circuit board designer Rick Hartley states, “The energy in the circuit is in the fields” [21:38:00].