I Power flow outside a wire - how close?

  • I
  • Thread starter Thread starter Joseph M. Zias
  • Start date Start date
AI Thread Summary
Power flow, as described by Poynting vectors, extends significantly beyond the wires in electric circuits, with energy spreading from the source to the resistors. Research indicates that while wire resistance causes some energy loss as heat, the majority of power flow occurs in the surrounding space. The analysis of energy distribution around a circuit suggests that power lines transmit energy across distances, although no energy streamlines begin or end on the wires themselves. The discussion highlights the need for clearer metrics, such as power per unit area, to quantify energy flow at various distances. Overall, understanding the spatial distribution of power flow remains an area that requires further exploration and clarification.
Joseph M. Zias
Messages
80
Reaction score
28
TL;DR Summary
power flow vs distance from wire
For at least a couple of decades a plethora of papers have presented power flow (via Poynting vectors) to be outside the wires. Wire resistance does cause some power to flow into the surface and cause heating, however. Given a DC circuit with low resistance wire I question how close to the wire is the power flow? Suppose a 10 volt source to 10 AWG wire with a 10 ohm resistor some distance away. What is the distribution of power vs perpendicular distance from the wire? So far, I have not seen this addressed.
 
Physics news on Phys.org
Joseph M. Zias said:
TL;DR Summary: power flow vs distance from wire
The Poynting flow of energy ##\vec{S}=\mu_{0}^{-1}\vec{E}\times\vec{B}## due to electric circuits generally extends to a rather large volume around the wires. This is can be seen from the figures in: Morris & Styer-Visualizing Poynting vector energy flow in electric circuits . To simplify the analysis to a 2D model over a finite region, the authors consider circuits consisting, not of conducting wires, but rather infinitely-long, conducting, hollow square cylinders with discontinuities on the boundary that represent voltage sources and resistances. Here's an example of the Poynting flow due to a battery connected to two resistors in series:
1687474535693.png

Evidently, the flow of energy spreads out from the source (the battery) to fill the space enclosed by the circuit and then converges into the sinks (the resistors). Of course, the details of 3D Poynting flow in the vicinity of a circuit of wires is more involved, but we can still anticipate that the lines of flow spread well away from the wires to fill both the interior and exterior of the circuit.
 
I note this is an undergrad research paper from 2000. Way to go Oberlin College. Great idea.
 
So, the analysis given suggest the power lines at the top of the poles are transmitting energy across the street? I will look into the reference given but at present I don't see any scale of watts/cm^3 at a given distance.
 
Joseph M. Zias said:
So, the analysis given suggest the power lines at the top of the poles are transmitting energy across the street?
Not true, at least to the extent that we can ignore the energy that's lost as heat in the power lines. Per the plot, no energy streamlines begin or end on the "power lines" themselves (i.e., the outer box, which is modeled as a perfect conductor), so no energy flows between any of the (perfect) conductors.
I don't see any scale of watts/cm^3 at a given distance.
(Note that your units here are misstated because they denote power per unit-volume. The Poynting vector tangent to the streamlines has units of power per unit-area or ##W/m^{2}## in SI units.) There are no units shown on the plot, but the text of Morris & Styer states:
1687662213447.png

so the spatial scale of the plot is established. But lacking something like a color scale that distinguishes the power flow in individual streamlines, the most we can say is that an overall power ##I^{2}R=0.5\text {W}## is delivered across space via 15 streamlines from the battery to each resistor. From that, depending on where you draw your cross-section and the distance between streamlines, from the plot you can guesstimate the average power flowing per unit-area.
 
Last edited:
Thread 'Motional EMF in Faraday disc, co-rotating magnet axial mean flux'
So here is the motional EMF formula. Now I understand the standard Faraday paradox that an axis symmetric field source (like a speaker motor ring magnet) has a magnetic field that is frame invariant under rotation around axis of symmetry. The field is static whether you rotate the magnet or not. So far so good. What puzzles me is this , there is a term average magnetic flux or "azimuthal mean" , this term describes the average magnetic field through the area swept by the rotating Faraday...
Back
Top