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Homework Statement
ok this is not a homework but i am confused by the derivation of ## f = \nabla (m . B)##
both start out with ##\vec B(r) \approx \vec B_0 + (\vec r' . \nabla)\vec B_0 ... \\
f = \iiint_{v'} \vec J( r') \times (\vec r' . \nabla)\vec B_0
##
where prime is body coordinates and unprime is space coordinates
the first one uses vector identities
##
(\vec r' . \nabla)\vec B = \nabla (\vec r' . B)  r' \times (\nabla \times B)
##
the other two terms die out because of different coordinates
then it proceeds to say curl of magnetic field is zero about the origin if it is due to external sources
then the proof proceeds i have posted in the photo
the second proof(from girffiths) uses le cevitas and kronecker deltas
while both seem to arrive at the same answer of ## f = \nabla(\vec m . B)## after this griffiths specifically mentions that
he mentions that ##\nabla \times B \neq 0##
honestly to me the first proof makes more sense because the magnetic field used is due to external sources and should not have curl at the origin but questioning seems griffiths seems inplausible so
what actually is correct sorry for the long post it has been bugging me for a long while now
Homework Equations
The Attempt at a Solution
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