Relativistic explanation for magnetic force between perpendicular wires

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Discussion Overview

The discussion revolves around the relativistic explanation for the magnetic force between perpendicular wires, focusing on the relationship between electric interactions and magnetism as described by relativity. Participants explore theoretical aspects and seek clarification on how these forces arise despite the perpendicular movement of charges.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how perpendicular wires can exert magnetic forces on each other, noting that length contraction does not occur in the direction of the current from any wire's reference frame.
  • Another participant references a lecture by Daniel Schroeder, suggesting that the electric fields of charges in the wire are distorted in the frame of a moving test charge, leading to a net force on the test charge.
  • There is a discussion about whether the deformation of the electric field is due to length contraction.
  • Several participants mention a textbook by Ohanian as a resource that covers the topic well, although there is uncertainty about the specific title and content.
  • One participant expresses interest in whether The Feynman Lectures would provide a good explanation of the concepts discussed.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and certainty regarding the relativistic effects on magnetic forces, with no consensus reached on the specific mechanisms or explanations. Multiple viewpoints and references to different resources are presented without agreement on a definitive explanation.

Contextual Notes

Some participants reference specific textbooks and lectures, but there is uncertainty about the details and whether they adequately address the original question. The discussion includes assumptions about the nature of electric fields and relativistic effects that remain unresolved.

guillefix
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I have read about how magnetism arises from electric interactions and relativity. But in that respect i don't see how perpendicular wires can exert magnetic forces on each other. The movement of the charges is perpendicular so length contraction does not occurr in the direction of the current for any of the wire electron's reference frames; and, as I have read this is the reason for magnetic forces.

How is this resolved?

Thank you,
 
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hi guillefix! :smile:

here's an image and commentary from daniel schroeder's 1999 summary lecture from edward purcell's 1960 book (http://physics.weber.edu/schroeder/mrr/mrr.html, link provided by Dalespam :wink:) …

fig6.gif


With all this in mind, let's now consider our wire again, but with the test charge moving directly toward it.

In the frame of the test charge the wire is moving downward. The negative charges in the wire, which are moving straight down, have their electric fields distorted as shown previously, but these fields are symmetrical from left to right so they exert no net horizontal force on the test charge. The positive charges in the wire, however, are now moving diagonally, so their fields are distorted as shown above. At the location of the test charge, the field of the positive charge to the right is stronger than that of the positive charge to the left, so the test charge feels a net force pushing it to the left.​

read the whole lecture! :smile:
 
Aah OK, I love diagrams :) So, is the deformation of the E field due to length contraction?

Yep, I'll definitivelly read the whole lecture, it looks really interesting!
 
This is covered brilliantly in a textbook by Ohanian.
 
Damn... I am not certain... I think it is called physics for engineers...something like that.
I had a copy and lent it to a student (you know the rest of the story!)
Ohanian textbooks are the best I have come across. I imagine the analysis is in the one you quote but I am not certain... I will get on Amazon and have a look
I have not looked at tiny tims reference yet but it looks good... I will look at it.
 
Last edited:
Tiny Tims reference is great... Ohanian includes more detail and more depth but the principle is the same.
 
Ok, id still like to know the book by Ohanian if you find it. BTW, would The Feynman lectures have a good explanation because I a copy of them. Anyway I'll find out coz I want to finish them soon :)
 

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