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 Sci Advisor PF Gold P: 2,056 Thide's treatment of magnetostatics 1) Thide assumes that each loop is a rigid object, so his force is a single value that acts upon the rigid body. You could ignore the (x) part of F(x), except that he uses it in the next equation below. 2) Hmm, I wonder if my draft version of his book downloaded years ago is different than the current version. I see that Eq. (1.15) is div B = 0. I can't access your link because my firewall at work blocks foreign sites, so I'll assume you are referring to Eq. (1.14) which is $$\mathbf{F}(\mathbf{x}) = J \oint_C d\mathbf{l}\times\mathbf{B}(\mathbf{x}) .$$Thide states earlier that he is considering small loops, so B from loop x' is assumed to be constant over all of loop x and vice versa.