I don't know how to build up Fourier series for this problem. I tried several times but no results. Can any body help me.(adsbygoogle = window.adsbygoogle || []).push({});

Consider the 2-d Laplace equation for the potential V(x,y) in the region inside

an empty square whose sides lie on the lines x = 0, x = a , y = 0, and y = a, respectively.

The sides at x = a , y = 0, and y = a are grounded, and

V(0,y) = C[itex]_{1}[/itex]sin[itex]\frac{(\pi)y}{a}[/itex] + C[itex]_{2}[/itex]sin[itex]\frac{2(\pi)y}{a}[/itex]

where C1 and C2 are constants

(a) Find V(x,y) everywhere inside the square.

Hint: use the trivial solution for X(x) with X(x)=0 at x=a

(b) Calculate the potential for C1=100V, C2=50V in the middle of the box. Do you find

any dependence on the box size?

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# Electrodynamics (Fourier)

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