- #1
Phrak
- 4,267
- 6
Maxwell's equations in integral form are not obviously local.
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?
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?