From: veritasium
The Poynting vector is a mathematical construct used in physics to describe the directional energy flux (the rate of energy flow per unit area) of an electromagnetic field [04:29:00]. It is represented by the symbol S [04:39:00] and is calculated using the cross product of the electric field (E) and magnetic field (B) [04:48:00]:
S = (1/μ₀) * (E x B) [04:41:00]
where μ₀ is the permeability of free space [04:46:00]. The direction of the Poynting vector indicates the direction of energy flow [05:11:00].
Historical Context
In the 1860s and 1870s, Scottish physicist James Clerk Maxwell made a significant breakthrough by realizing that light consists of oscillating electric and magnetic fields [03:22:00]. These fields oscillate perpendicular to each other and are in phase [03:36:00]. Maxwell developed equations, now known as Maxwell’s equations, that govern the behavior of these electromagnetic fields and waves [03:45:00].
In 1883, John Henry Poynting, one of Maxwell’s former students, applied the principle of conservation of energy to these fields [03:55:00]. He theorized that if energy is locally conserved, its path of flow from one place to another should be traceable [04:02:00].
Energy Flow in Light
For light, the Poynting vector demonstrates that energy flows perpendicular to both the electric and magnetic fields, in the same direction that light travels [05:17:00]. This means light carries energy from its source to its destination via its electric and magnetic fields [04:13:00].
Crucially, Poynting’s equation applies not only to light but to any scenario where electric and magnetic fields coincide [05:39:00]. Wherever these fields exist together, there is a flow of energy that can be calculated using the Poynting vector [05:49:00].
Energy Flow in Electric Circuits
Contrary to common misconceptions, electrical energy in circuits is primarily carried by electromagnetic fields outside the wires, not by the electrons within them [02:09:00].
Common Misconceptions
Many people are taught that:
- Electrons themselves possess potential energy [03:01:00].
- Electrons are pushed or pulled through a continuous conducting loop [03:05:00].
- Electrons dissipate their energy directly in the device [03:08:00].
This understanding is incorrect [02:09:00]. There are physical gaps in electrical lines, such as transformers, where electrons cannot flow continuously [02:13:00]. Additionally, if electrons carried the energy, it would be difficult to explain why energy flows only one way (from source to device) when electron flow can be bidirectional (as in AC) [02:34:00].
How it Actually Works
In a simple DC circuit (e.g., a battery and a light bulb):
- When a battery is connected, its electric field extends through the circuit at the speed of light [06:13:00].
- This electric field causes electrons to accumulate on certain conductor surfaces (making them negatively charged) and deplete from others (leaving them positively charged) [06:20:00].
- These surface charges create a small electric field inside the wires, causing electrons to drift slowly (around 0.1 mm/s) in one direction, forming the current [06:34:00].
- The surface charges also create an electric field outside the wires [06:58:00].
- The current inside the wires creates a magnetic field outside the wires [07:05:00].
- The combination of these electric and magnetic fields in the space around the circuit results in a flow of energy, as described by the Poynting vector [07:10:00].
Using the right-hand rule for the cross product (E x B), the energy flux can be visualized:
- Around the battery, energy flows radially outwards into the fields [07:26:00].
- Along the wires, energy flows in the direction of the circuit [07:49:00].
- At the light bulb filament, the Poynting vector is directed inward, meaning the light bulb receives energy from the surrounding fields [08:00:00].
Energy takes many paths from the battery to the bulb, but in all cases, it is transmitted by the surrounding electric and magnetic fields [08:13:00]. Even though electrons may move in two directions (away from and towards the battery), the energy flux, as determined by the Poynting vector, flows in only one direction: from the source to the device [08:45:00]. This confirms that the fields, not the electrons, carry the energy [08:56:00].
Alternating Current (AC) Circuits
The same analysis holds true for AC circuits [09:29:00]. While the current direction reverses every half cycle, causing both the electric and magnetic fields to flip simultaneously, the Poynting vector still points in the same direction: from the source to the load [09:13:00]. This explains how power lines transmit energy from power plants to homes; electrons merely oscillate back and forth within the wires, but the oscillating electromagnetic fields outside the wires carry the power [09:35:00].
Real-World Validation: Submarine Cables
The practical importance of understanding energy flow through fields was highlighted during the laying of early undersea telegraph cables [10:13:00]. The first Transatlantic cable, laid in 1858, suffered from severe signal distortion and lengthening, making it difficult to differentiate messages [10:18:00].
A debate ensued among scientists:
- William Thomson (Lord Kelvin) believed electrical signals moved like water through a rubber tube [10:47:00].
- Others, like Heaviside and Fitzgerald, correctly argued that it was the fields around the wires that carried the energy and information [10:56:00].
The latter view proved correct [11:05:00]. The problem with the cable was its design: the central copper conductor was coated in an insulator and then encased in an iron sheath [11:10:00]. Although intended for strength, the conductive iron interfered with the propagation of electromagnetic fields by increasing the capacitance of the line [11:19:00]. This historical event demonstrated that understanding the behavior of fields is crucial for effective energy transmission.
This is also why modern power lines are suspended high above the ground, maintaining a large insulating gap of air, as even damp earth can act as a conductor and interfere with the fields [11:27:00].
The Long Wire Circuit Thought Experiment
Consider a hypothetical circuit with a battery, a switch, a light bulb one meter away, and two wires each 300,000 kilometers long (the distance light travels in one second) [00:00:03].
When the switch is closed, the light bulb lights up almost instantaneously, in approximately 1/C seconds [11:45:00]. This is because the limiting factor is not the travel of an electric field down the wire for a light-second, but rather the propagation of the electric and magnetic fields through the space around the wires to the light bulb, which is only one meter away [12:07:00]. These fields can reach the bulb in a few nanoseconds [12:20:00].
This thought experiment further illustrates that the energy is delivered by the traveling electromagnetic waves around the power lines, not by the flow of electrons through the wires [12:20:00].