Vector Wave Equation: Uses & Benefits

[wasi-uz-zaman]

hi, my question is , when do we need to have vector wave equation. So far in Maxwell equation you can find scalar as well as vector wave equation, I figure out when we are looking for the scattering we need vector wave equation. Second isn't simple to work out scalar potential and then by its gradient we can have electric field and so on.

 

[DevacDave]

You need it pretty much all the time where it is the resulting solution of a partial differential equation. You will encounter them everywhere from hydrodynamics to electrodynamics (fiberoptics for a textbook example), really.

As of the difficulty of working them out, sometimes it is the only way to get the rigorous solution. There is a whole discipline focusing on it called potential theory (related to harmonic analysis).

Does it answer your question or did I misunderstood you?

 

[wasi-uz-zaman]

thanks dear - very much clear

 

[DevacDave]

I forgot about one more method of solution. Much less strict, but more than enough for a lot of the problems that can be, very crudely, summarised as "there may be an analytic exact solution but we can't find it": Inverse Problems. If you have an approximate model and some of the eigenvalues (observed results) than you can recreate the problem statement in detail. Perhaps even find the exact solutions.

However it is not my area of study, I have only recently began to read some of the introductory books on the topic (I'm just past the second chapter in "http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/Books/index.html " by prof. Tarantola) From what I have gathered up to this point, it is largely the tool of geophysicists and they are in all likelihood best suited to lay it down for you if I got you interested.

 

[wasi-uz-zaman]

sure, why not I will download the book of " Inverse Problem theory" and than will discuss with you after completing my current project.
thanks