Boundary Conditions

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Does anyone here have a copy of Griffith's E&M?

On page 128, condition III V=V_0 (y) when x = 0.

Do you know why then value V_0(y) does not appear in in equation 3.28, V(x,y) = Ce^(-ky)sin(ky)?

The author does not explain this.
 

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  • #2
vanhees71
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Have you read the solution to the end carefully? (3.28) gives you an infinite set of solutions given the separation ansatz (3.22), working in the boundary conditions (i) and (ii). Now you can get any solution by an infinite series as explained just in the following paragraphs. Then you can use the boundary condition (iii) to define the corresponding coefficients in the general series, which here is a Fourier series in the narrow sense. The general technique of separation of variables to solve PDEs leads to generalized Fourier-series expansions, which is a very important technique in theoretical physics. You should thus carefully study this (in my opinion very nicely explained) example in Griffiths's textbook!
 

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