The discussion revolves around the derivation of the force on a magnetic dipole, specifically the expression \( f = \nabla (\vec{m} \cdot \vec{B}) \). Participants are examining two different proofs that arrive at this result, one assuming the curl of the magnetic field is zero and the other not making this assumption.
Some participants express confusion about the implications of Griffiths' proof and whether it can be reconciled with the first proof. There is an ongoing exploration of how to continue the first proof without assuming the curl is zero, with some guidance provided on potential manipulations and identities that could be used.
Participants note that the magnetic field in question is due to external sources, which may influence the curl at the location of the dipole. There is also mention of specific examples from Griffiths' text that illustrate scenarios where the curl is non-zero.
Here, the notation ##\nabla B## is not the dyadic formed from ##\nabla## and ##B##. So, here,timetraveller123 said:wait i was looking through wikipedia and found this
this seems to suggest
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(A \cdot \nabla)B
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is not
##
A \cdot (\nabla B)
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