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Geometric transformation of E field to B ?

  1. Feb 1, 2016 #1
    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?
  2. jcsd
  3. Feb 1, 2016 #2
    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.
  4. Feb 1, 2016 #3


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    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/ .
  5. Feb 1, 2016 #4
    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.
  6. Feb 1, 2016 #5


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    According to numerous posts on PF, Griffiths does cover this topic in a manner similar to Purcell.
  7. Feb 1, 2016 #6
    It's not in chapter 5, maybe chapter 12 which introduces relativity.
  8. Feb 6, 2016 #7
    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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