Magnetic Moment Definition Verification/ Proof

by cubejunkies
Tags: definition, magnetic, moment, proof, verification or
 P: 34 I saw the equation here http://en.wikipedia.org/wiki/Magneti...oop_definition for the definition of the magnetic moment for a non-planar loop. Can someone tell me if there's a name for this equation $m= \frac { I }{ 2 } \int { \overrightarrow { r } } \times d\overrightarrow { r }$, if it's even right, and where I could find a derivation and/or proof of the equation? I've been fumbling over this for several hours now and I've gotten absolutely nowhere. I don't have any access to any texts on the matter, all I have is google and wikipedia at the moment. Thanks Anthony
 Sci Advisor HW Helper PF Gold P: 2,007 It follows from $${\bf m}=\frac{1}{2}\int{\bf r\times j}d^3r$$ with the substitution $${\bf j}d^3r\rightarrow I{\bf dr}.$$ The derivation of the j equation takes about one page in an EM textbook. It is on J. Franklin, "Classical Electromagnetism" on page 212. Your equation is derived directly on page 210. You should also know that $$\frac{1}{2}\int{\bf r\times dr}=$$ the area of the loop.