Geometric transformation of E field to B ?

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Discussion Overview

The discussion revolves around the relationship between electric fields (E fields) and magnetic fields (B fields), particularly how motion of a test charge generates a circulating magnetic field. Participants explore whether this phenomenon can be understood geometrically and if it can be termed a 'transformation'. The conversation touches on theoretical concepts, references to textbooks, and the implications of relativity.

Discussion Character

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

Main Points Raised

  • One participant notes that a stationary test charge generates an E field with zero curl, while motion generates both an E field and a circulating magnetic field B, questioning the geometric reasoning behind this.
  • Another participant asserts that moving an electric field changes it, leading to the generation of a magnetic field, referencing Maxwell's equations as a well-understood framework for this relationship.
  • Some participants emphasize that relativity is the fundamental reason for the generation of the magnetic field due to motion, citing Purcell's textbook as a classic presentation of this concept.
  • A participant expresses gratitude for the reference to Purcell and mentions working through Griffiths' Electricity and Magnetism, indicating a perceived gap in Griffiths' treatment of the topic.
  • Others challenge the assertion about Griffiths' coverage, suggesting that it does address the topic similarly to Purcell, but may be located in different chapters.
  • Further clarification is provided that Griffiths does cover the transformation from E to B in chapter 12, but there is uncertainty about the depth of treatment compared to Purcell.

Areas of Agreement / Disagreement

Participants exhibit a mix of agreement and disagreement regarding the coverage of the topic in Griffiths' textbook and the clarity of the geometric reasoning behind the generation of magnetic fields from moving electric fields. The discussion remains unresolved on some aspects, particularly the depth of treatment in different textbooks.

Contextual Notes

There are limitations regarding the assumptions made about the understanding of calculus and the specific chapters of textbooks referenced. The discussion also reflects varying interpretations of the relationship between electric and magnetic fields without reaching a consensus on the geometric reasoning involved.

Ghost117
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When a test charge is stationary, it generates an E field with zero curl.

When it moves, it generates a circulating magnetic field B...( as well as the E field.)

Is there a geometric reason for this? How does motion alone generate a circulating field B?

Can we call this change a 'transformation' even?
 
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By moving an electric field, you are changing the electric field. A changing electric field is essentially a magnetic field.

Not sure how much calculus you know, but this is very well-understood. The relationship is described in Maxwell's equations.
https://en.wikipedia.org/wiki/Maxwell's_equations
 
Ghost117 said:
Is there a geometric reason for this? How does motion alone generate a circulating field B?

The fundamental reason is relativity. The textbook by Purcell, Electricity and Magnetism, is the classic presentation of this. For a similar presentation, see section 23.2 of my book Light and Matter: http://lightandmatter.com/lm/ .
 
bcrowell said:
The fundamental reason is relativity. The textbook by Purcell, Electricity and Magnetism, is the classic presentation of this. For a similar presentation, see section 23.2 of my book Light and Matter: http://lightandmatter.com/lm/ .

Thanks much, that's what I needed i.e. a text that deals with this. I'm working through Griffiths E&M right now and I don't think he deals with it.
 
According to numerous posts on PF, Griffiths does cover this topic in a manner similar to Purcell.
 
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marcusl said:
According to numerous posts on PF, Griffiths does cover this topic in a manner similar to Purcell.

It's not in chapter 5, maybe chapter 12 which introduces relativity.
 
Ghost117 said:
It's not in chapter 5, maybe chapter 12 which introduces relativity.

p.s. By the way, it is in Griffiths chapter 12, pretty much the last section of the last chapter, has a section on the transformation from E to B. However, I think bcrowell was referring to purcell because that would deal with it in more depth.
 

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