Poynting Theory Paradox

How a Simple Circuit Thought Experiment Reveals the Strange Reality of Energy Flow

Introduction

Imagine this setup: you connect a lightbulb to a power source using a pair of wires. The lightbulb is only 10 feet away from the power source, but instead of using a direct path, you run the wires in a loop that stretches out to a full mile before coming back. You flick the switch — and the bulb lights up.

But this raises a confusing question:
Did the energy take the short 10-foot path through the air, or the long 1-mile journey through the wires?

Most people assume the energy somehow "jumps" the short physical gap. But Poynting theory (PT) gives a very different and more accurate answer — and it reveals something profoundly unintuitive about how circuits really work.

The Misconception: Energy Flows Through the Wire

In standard explanations, energy is pictured as moving through the wire — as if electrons zip along like water in a pipe. This picture is wrong in both speed and substance:

• Electrons move very slowly (inches per minute in DC).
• In AC, they simply wiggle back and forth.
• The bulb lights up before any single electron from the power source gets near it.

So what actually delivers energy to the bulb?

Poynting Theory: Fields Deliver Energy Through Space

Poynting theory, developed by John Henry Poynting in the 1880s, describes energy flow in electromagnetic systems using the Poynting vector:

\[ \vec{S} = \vec{E} \times \vec{B} \]

This cross product of the electric field \( \vec{E} \) and magnetic field \( \vec{B} \) gives a directional energy flow vector \( \vec{S} \) — pointing not along the wire, but into the space around it.

So where does the energy flow?

• It flows through the space surrounding the wires, following the guided geometry of the circuit.
• The energy doesn’t go “through” the wire like fluid; it moves alongside it, riding the fields shaped by voltage and current.

In our case, the mile-long wires determine the energy’s route — not the 10-foot physical distance between power source and bulb. The energy flows around the entire loop, taking the long way.

Why the Bulb Doesn’t Light Instantly

Even though the bulb is physically close, it doesn’t receive power until the electromagnetic field has propagated through the entire wire path. This propagation occurs at nearly the speed of light, but it still requires the field to reach the load through the full circuit geometry.

Energy doesn't care about physical distance — it follows the path defined by the fields, not by proximity.

Implications for Our Understanding of Circuits

• Wires are guides for fields, not pipelines for energy.
• Energy flows in the space around the wire, directed by the electric and magnetic field structure.
• Wire length matters: longer wires shape larger and more complex field geometries.
• Circuit behavior is field-driven; “current” is a local response to field propagation.
• This view aligns with our understanding of antennas, RF systems, and wireless energy transfer.

Conclusion: The Long Way Is the Real Way

The 10-foot bulb, 1-mile wire paradox illustrates a deep truth: electricity is a field phenomenon, not a matter of particles traveling from source to load. Poynting theory shows that the energy flows through the space around the wires, following the circuit path defined by their shape, not their proximity.

So the next time someone asks where the energy flows, you can smile and say:

“It takes the long way — through the fields.”

References and Further Reading

• J.H. Poynting, “On the Transfer of Energy in the Electromagnetic Field,” Philosophical Transactions of the Royal Society A, 1884. DOI link
• MIT OpenCourseWare – Electromagnetic Energy and Poynting Vector: MIT Lecture
• “Where Does the Energy Flow in a Circuit?” by Veritasium (YouTube): Watch here
• Purcell & Morin, *Electricity and Magnetism*, 3rd Edition, Cambridge University Press
• James Redgewell, “Deep Thinking on Capacitive and Inductive Coupling in Electrical Circuits, Part 5,” 2025. [Author's Blog]