When to Use Differential vs. Integral Form of Maxwell's Equations?

[bman!!]

hello.
i know that the differential form of maxwells equations is generally considered the most elegant and for the most part are easier to apply to most problems, and whichever one you choose integral or differential form you can always work through it.

i was wondering if anyone had any useful rules of thumb for which problems are better suited to differential form and which ones are better suited for integral form?

cheers

 

[merryjman]

IMO, the differential form is more useful when dealing with charge densities and current densities, whereas the integral form is more useful for specific charges and currents. I also think the Diff form is better for describing the behavior of E/D-fields and B/H-fields (i.e. E-fields diverge whereas B-fields curl) and the Int form is better for describing flux and the things that caused the fields. Finally, in Diff form for empty space it is easy to see why Ampere's law (prior to Maxwell's fix) practically begged for a time-varying electric field term, since it would make the symmetry between E&B complete.