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I cannot for the life of me wrap my head around the idea of a boundary condition. I understand the idea (at least I think I do) of solving a differential equation with given initial conditions. But is solving for a magnetic field or electric field while enforcing boundary conditions sort of the same thing? If so, why is it solved in terms of its perpendicular and parallel components?

I read at one point that the purpose of a boundary condition is so specify a "point in space" or to obtain a sense of direction/position when solving for a magnetic or electric field when given a specific geometry. Makes sense to me: it would do no good to just say a magnetic field is n-amount Gauss or Teslas. But isn't that why we use coordinate systems? I guess I just don't understand the idea of "enforcing boundary conditions in order to solve a problem." ....

The best I can make of it is perhaps, hypothetically, if a current or charge density is specified upon a surface with a known geometry, then do you use that to extrapolate information for the B-Field and E-field....(i.e. field will be 0 here....will also flow in this direction...etc ..) But if so, how does all the parallel and perpendicular stuff come in?

I apologize for the convuluted way I've asked this question. I think the problem is more that I'm confused to the extent that I don't even really know HOW to ask the question. So hopefully, if someone is patient enough with me...I can weed through this boundary conditions business.

Thanks for everything. You guys are great!

~**S