1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Analogy between E and B fields

  1. Jun 15, 2008 #1

    I was simply wondering this for some time now... I am constantly seeing similarities between electric (E) fields and magnetic (B) fields.

    A few examples, Coulomb's law and Biot-Savart's law:
    [tex]dE = \frac{1}{4 \pi \epsilon_0} \frac{dQ}{r^2}[/tex]
    [tex]dB = \frac{\mu_0}{4 \pi} \frac{I dl}{r^2}[/tex]

    They are nearly the same... Especially the constants [itex]\mu_0[/itex] and [itex]epsilon_0[/itex], they always seem to be taking eachother's place, where [itex]epsilon_0[/itex] is always replaced with [itex](\mu_0)^{-1}[/itex] (not just in this example but everything I have ever come across, like in EM-waves etc...)

    Also in the case of time-varrying E or B fields they seem to be related, you can't only look at one without considering the other anymore (maxwell equations etc)...

    I have heard / read a bit about this and it seems to be that E and B fields are essentially the same, in quantum mechanics, or in (general?) relativity (or both? I dunno..)...
    Is this true?

    If anyone has some information on this that would be great, I'm very interested in this...

    I don't know if it's the same with you guys but for some reason I cannot see the latex images in my post... Seems to be something wrong...
  2. jcsd
  3. Jun 15, 2008 #2
    The electric and magnetic fields are unified in special relativity.

    It is possible to derive the Biot-Savart law using a thought experiment with Coloumb's law and a moving observer. When we use the Lorentz transformations of special relativity to transform coordinates, the Biot-Savart law is the result.
  4. Jun 15, 2008 #3
    Is this transformation difficult to actually calculate? Could you perhaps show an example?
  5. Jun 15, 2008 #4


    User Avatar
    Homework Helper
    Gold Member

    The transformation is not too difficult, but it could take some time to reproduce it here on the forum. I suggest trying google first, or checking out Chapter 12 of Griffth's "Introduction to Electrodynamics" if available.

    For instance, here is a talk given by Daniel Shroeder from Weber State on this topic:

    Last edited: Jun 15, 2008
  6. Jun 15, 2008 #5
    Thanks that seems like an interesting read!
  7. Jun 17, 2008 #6
    I don't happen to have a Griffith. I do, however understand the vacum gauge symmetry of E and B. Does Griffith discuss any non-vacuum symmetry? just curious...
  8. Jun 17, 2008 #7
    Electricity and magnetism are two extremes of the same phenomenon (electromagnetism). If you were to approach this quantum mechanically, with the addition of a few things, Maxwell's equations will show them to be practically identical. So then why is there a magnetic force and electric force...actually...I don't know and I have not gone into quantum mechanics...but it has something to do with charges moving, so I would assume magnetic fields occur due to moving Electric Fields...and if electric fields move, they are not always constant in a fixed frame of reference...and so magnetic fields occur essentially when there is a changing electric field...and electric fields occur with changing magnetic fields, which is apparently symmetric.
  9. Jun 18, 2008 #8
    Yes, we are not talking about the vacuum guage symmetry, but rather a process of deriving the magnetic field of a infinite line of current using the lorentz transformations and coloumb's law.
  10. Jun 18, 2008 #9
    Yes, of course. My mistake. Checking my notes, the gauge doesn't enter into it, apparently. It seems however, that if
    [tex]dE = \frac{1}{4 \pi \epsilon_0} \frac{dQ}{r^2}[/tex]
    is expressed in a coordinate independent form using
    [tex]d*F=-*J[/tex] where J is a 1-from,
    [tex]dB = \frac{\mu_0}{4 \pi} \frac{I dl}{r^2}[/tex]
    will be included in the same equation, where the Lorentz transform is implicit. I can't simply tell by looking as these two equations if that would be the case.
  11. Jun 19, 2008 #10
    Another one

    There's Another similarity between the Gauss' And Amperean laws

    Integral(closed surface) E.ds = q(enclosed)/Epsilon nought

    Integral(closed loop) B.dl= I(enclosed)/Mu nought
  12. Jun 19, 2008 #11
    I know, there are loads, and it's obvious from the maxwell equations that time-varying E and B fields are physically connected. However it is not directly obvious that they would be the same thing (if you look at it in the right way)...
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook