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Faraday's Law, a good enough example, in differental form is

[tex]\partial_i B_j - \partial _t E_k = J_k[/tex]

where (i,j,k) are cyclic permutations of (x,y,z).

In integral form,

[tex]\frac{d\Phi}{dt} = \oint E \cdot dl[/tex]

The potential around a closed loop is equal to the time rate change of a nonlocal magnetic flux.

Of course, as the integral form is equivalent to the differential form it must be local. What am I missing?? What connects the nonlocal \Phi to the local B?