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!

Derivation for Magnetic Field Due to Dipole

  1. Apr 13, 2009 #1
    I am looking for a reference (derivation) for this exact formula given for "the magnetic field due to a dipole [tex]\mu[/tex] fixed at the origin" :

    [tex]B=-\frac{\mu}{R^3}+\frac{3r(\mu\cdot r)}{R^5}[/tex]

    I don't really know anything about dipoles or how they are derived (I have only taken lower division E&M) so the [tex]\mu[/tex] has no meaning to me. It seems that this formula is derived from a vector potential [tex]A=\frac{\mu\times r}{r^3}[/tex] and I know that B = grad x A so it might help more to understand what this potential actually means as well as a good lesson on what is the dipole vector mu. Thanks.

    note:i'm having trouble rendering the tex so here is the formula in plain text:

    B=-u\R^3 + (3r(u dot r))\R^5 here i use small r for the position vector and R for the length of r and u stands for the greek letter mu for the dipole vector.
    Last edited by a moderator: Apr 13, 2009
  2. jcsd
  3. Apr 13, 2009 #2


    User Avatar

    Staff: Mentor

    I know it's in Griffiths's "Introduction to Electrodynamics." It's probably in other intermediate-level E&M textbooks such as Purcell or Lorrain & Corson.

    Griffiths does it as part of the general "multipole expansion" of the magnetic vector potential from a general distribution of current. You might try a Google search for something like "magnetic vector potential multipole expansion."
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook