Why do we need boundary conditions in Physics? Its significance?

[vinzie]

Well as the topics says I need a clarification why do we need the so called boundary conditions?

I have seen it in electostatics, magnetostatics etc.
I tried in many ways to get that stuff into my head, but its just only banging my head not getting into.. I really wana know what is that and what is its significance in physics?

What is this continuous and discontinuous thing mentioned in boundary conditions?

Thanks in Advance!

 

[phinds]

It would be helpful if you would say how far along you are in math and physics. What level courses have you taken?

 

[gnurf]

Well as the topics says I need a clarification why do we need the so called boundary conditions?

You need boundary conditions because Maxwell's Equations in integral form involve closed paths and surfaces that might or might not encompass a boundary between two different media. The boundary conditions relate the field components on one side of the boundary to the corresponding point adjacent to and on the other side of the boundary.

 

[vinzie]

Hi,

I have just started doing graduation in physics. This is my first year. Electricity and magnetism is one of the papers.

In mathematics I know Integration and Differentiation at basic level.

Might be I could understand this stuff, If I get to know about continuity and discontinuity.

Thanks

 

[gnurf]

Hi,

I have just started doing graduation in physics. This is my first year. Electricity and magnetism is one of the papers.

In mathematics I know Integration and Differentiation at basic level.

Might be I could understand this stuff, If I get to know about continuity and discontinuity

In that case electromagnetics might not be the most intuitive place to begin to understand boundary conditions. Unlike this cantilever example, where just by looking you can see that the deflection at W=0 must be zero, the boundary conditions in EM arise form the application of Maxwells laws on different (not necessarily difficult) geometries. I could tell you that the discontinuity between two tangential H-field components at a boundary is equal to the surface current density at that point, but this probably does not help you at all.

 

[Floid]

Depends on what you mean by boundary conditions:

If you mean the boundary conditions, as in points of a defined value used to solve equations then they are required to find particular solutions to many PDEs in electromagnetics. Without the boundary conditions, there are an infinite number of solutions to the PDEs which isn't really that interesting. But given the boundary conditions, a unique solution can be obtained for the given boundary conditions (which is interesting).

An example would be solving for voltage at all points in an area using Laplace's equation. Given the boundary conditions of the edges of that area, the voltage at all points within it can be found.


If you are talking about boundary conditions as in the boundary between two areas of different dielectric permitivity (among other examples) then the ideas are important because it isn't immediately apparent what happens when the underlying conditions assumed in particular equations change. So a lot of effort is given to determining what happens on these boundaries.

 

[vinzie]

Hi Thanks to All!

phinds, gnurf, floid, for taking time to clarify my question?

From your clarifications, I got where to head...

So far, according to my perceptions, boundary conditions are needed in electrostatics and magnetostatics as its laws were derived for closed paths and surfaces.

And I believe to understand it clearly I need to go through some calculus. Hope I will get through this stuff!

Thanks! :!)