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There are two types of questions I can't figure out how to answer...

the first is this one:

Find the potential between two parallel planes. The first is in x=0, the second in x=L.

[itex]\Phi(x=L)=\Phi_0 |sin(ky)|[/itex]

and

[itex]\Phi (x=0)=0[/itex]

What I thought I should do is look for a solution of the sort:

[itex]X(x)=Ae^{\sqrt{k^2+l^2}}+Be^{-\sqrt{k^2+l^2}}[/itex]

[itex]Y(y)=Csin(ky)+Dcos(ky)[/itex]

[itex]Z(z)=Esin(lz)+Fcos(lz)[/itex]

Then, I should start checking which of the terms should vanish.

But when I looked at the published solution, it was completely different:

[itex]|sin ky|=\sum_{n=0}^{\infty}{A_ncos(2kny)}

[/itex]

[itex]\rightarrow |sin(ky)|=\frac{2}{\pi}+\sum{\frac{4}{\pi(1-4n^2)}}cos(2kny)[/itex]

So now we seek a solution for Laplas eq. this way:

[itex]\Phi(x,y)=C_0x+\sum_{n=1}^\infty{C_n(x)cos(2kny)}[/itex]

and:

[itex]\frac{d^2}{dx^2}C_n =(2kn)^2C_n[/itex]

I don't understand this solution at all.

Why should one expand this function, |sin(ky)| ?

and what is the last equation:

[itex]\frac{d^2}{dx^2}C_n =(2kn)^2C_n[/itex]

Thank you so much!

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# Potential between two parallel planes

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