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Homework Help: Magnetic dipole derivations

  1. Mar 9, 2007 #1
    this is not homework help.I want to know.

    Hello,can any one suggest why for a dipole m placed in a magnetic field B
    F=grad(m.B)
    and N=mxB?
     
  2. jcsd
  3. Mar 9, 2007 #2

    siddharth

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    Take an infinitesimal current loop of arbitrary shape and use the Lorentz force law.
     
  4. Mar 9, 2007 #3

    Meir Achuz

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    That will work, but the derivation is a bit involved for an arbitrary shape.
    If you are satisfied with doing it for a rectangular loop, that is easier for the torque. Once you know the torque, you can show U=-mu.B, and then
    use F=-grad U.
    If you model the magnetic dipole as two magnetic poles, then the derivations are just the same as for electric dipoles, which are easier.
     
  5. Mar 9, 2007 #4
    To Siddharth:I found your approach in jackson.However,Griffiths also asks in his exercise to do in the same way.Only Jackson used J while Griffiths prefers I (in his hint).
    I got upto:
    F=I* closed int{dl x [(r. grad_0)B](r_0)} where dl is infinitesimal loop element; and the right portion is obtained after Taylor series expansion.
    Now griffiths and Jackson says to use Levi-Civita symbols...
    I was trying to insert the result: vector area a= (1/2)int{ r x I) inside the integral extracting (dl x r) so that I can get 'a' inside the integral and then have dm inside.But got stuck.It appears I am near the way but cannot get it.
    Please help.

    The other approach ultimately assumes F=grad(m.B).So, I prefer not to use it.
     
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