Energy Flow in Circuits — The “Weird Truth” (Feynman / Maxwell / Poynting)

1. The Core Idea (The Big Shock)

👉 Energy does NOT flow inside the wire.
👉 Energy flows in the electromagnetic field around the wire.

• The wire is not a pipe carrying energy

• The wire is a guide for fields

• The energy travels in space, not in the copper

The wire is like a rail.
The electromagnetic field is the train.

🧠 2. Why This Feels Wrong

We are taught:

• Electrons move → carry energy → power the load

But this breaks down:

⚡ Problem:

• Electrons drift extremely slowly (mm/s or less)

• Yet the light turns on almost instantly

👉 So electrons cannot be delivering energy physically from source to load.

⚙️ 3. What Electrons Are Actually Doing

Inside the wire:

• Electrons move randomly at ~1,000,000 m/s (thermal velocity)

• But in all directions equally → cancels out

Then:

• A tiny bias (drift velocity) is added by voltage

• This drift is extremely slow

Analogy:

• Crowd running randomly in a station = thermal motion

• Slight lean in one direction = current

👉 Current is just a tiny imbalance, not bulk transport of energy

⚡ 4. The “Marble Tube” Explanation (and its limitation)

Common explanation:

• Push one electron → pushes next → chain reaction

✔️ True: signal propagates fast (~2/3 speed of light)
❌ Misleading: suggests energy flows through electrons

Key Question:

If electrons are everywhere in the loop…

👉 How does energy know to go only from battery → bulb?

📡 5. Maxwell’s Breakthrough

Maxwell’s equations showed:

• Electric fields create magnetic fields

• Magnetic fields create electric fields

👉 This produces self-propagating waves

Result:

• Energy can travel through empty space

• No medium required

👉 This is electromagnetic radiation—and also what happens in circuits

🧭 6. The Poynting Vector (The Key Tool)

Physicist John Henry Poynting defined:

👉 Energy flow = cross product of electric and magnetic fields

• Direction = where energy flows

• Magnitude = how much energy per area

This is called the Poynting vector

🔌 7. What Happens Around a Wire

Around a current-carrying wire:

Electric field (E):

• Along the wire (drives current)

• Radially outward (due to surface charges)

Magnetic field (B):

• Circles around the wire

🧠 Combine them:

👉 E × B = energy flow

Result:

➡️ Energy flows from space INTO the wire

Not along it.

🔥 8. At the Load (Resistor / Bulb)

At the bulb:

• Energy comes from all directions

• Flows inward from surrounding space

• Gets converted into:

  • Heat

  • Light

👉 The wire is not delivering energy
👉 The field is feeding the load

🧲 9. The Role of Surface Charges (Hidden but Critical)

Very important (often ignored):

• Tiny charges build up on the surface of the wire

• They are not uniform

• They create a gradient along the wire

What they do:

• Shape the electric field inside AND outside the wire

• Control where energy flows

👉 Without them:

• No structured field

• No controlled energy transfer

🔄 10. Why You Still Need the Wire

Good question:
👉 “If energy flows in space, why use wires?”

Because:

1. Wire → allows current

2. Current → creates magnetic field

3. Electric + Magnetic fields → create energy flow

Without wire:

❌ No current
❌ No magnetic field
❌ No Poynting vector
❌ No usable energy flow

⚡ 11. What Happens When You Flip a Switch

Sequence:

1. Electric field changes

2. Change propagates at ~speed of light

3. Field reaches bulb almost instantly (~nanoseconds)

4. Energy starts flowing immediately

Important:

• Light appears before electrons complete the loop

• Full brightness takes longer (steady state)

👉 Energy arrives via the field, not electrons

🔁 12. Steady-State vs Transient

Initial:

• Field propagates through space directly

Steady state:

• Fields stabilize

• Continuous energy flow maintained

📡 13. Coaxial Cable (Perfect Example)

In a coax cable:

• Inner conductor + outer shield

• Field exists only between them

👉 Energy flows entirely in the empty space between conductors

Not in the metal.

Key insight:

Engineering a cable = engineering the space where the field lives

🌀 14. Even Stranger: Circulating Energy & Momentum

In some systems (charge + magnet):

• Energy can flow in closed loops

• No work is being done

• But energy still “moves”

👉 This energy carries real momentum

• Even angular momentum

• Measurable in experiments

🧠 15. Final Mental Model

❌ Old model:

• Electrons carry energy through wire

✅ Better model:

• Battery creates electric field

• Current creates magnetic field

• Fields combine → energy flow

• Energy travels in space

• Wire guides and shapes the field

🧾 16. One-Line Summary

Energy in circuits flows in the electromagnetic field around the wires, guided by them—not inside them.

💡 Braarud Smie Takeaway

Even though energy flows in the field:

• Wires still matter A LOT:

  • Cross-section → current handling

  • Insulation → voltage safety

  • Mechanical strength → durability

👉 The wire doesn’t carry the energy
👉 But it controls how the energy flows