Which Form of Maxwell's Equations is More Useful? (Integral versus Differential)

[kent davidge]

There are two forms of the Maxwell equations, one is the differential form, the other is the integral form. Which one is more useful?

 

[Vanadium 50]

Depends on the problem you are trying to solve.

 

[rude man]

I like the differential form because (1) they apply to every point in space, not just some volume or surface; and (2) with just two purely mathematical relations, to wit, the Stokes and divergence (aka Gauss's) theorems, all the integral relations are immediately derivable from the differential ones.

 

[vanhees71]

The fundamental form of the Maxwell equations is the local, i.e., differential form. A local field theoretical description is in a sense the natural mathematical form for relativistic field theories, and Maxwell's electromagnetism is a paradigmatic example for a relativistic field theory.