V = 0 y L V = Vo V = 0 L x V = 0 Each side of a square pipe, side length L, is kept fixed at a particular potential, either V = 0 or V = Vo where Vo is a constant, as shown in the figure. Using the separation of variables technique, show that V(x, y) at all points inside the charge-free square is given by: V(x, y) = Σ 4Vo sin пп L 'n#r\sinh(nTy/L) sinh(nữ) n=1,3,5,...

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V = 0
y
L
V = Vo
V = 0
L
x
V = 0
Each side of a square pipe, side length L, is kept fixed at a particular potential, either
V = 0 or V = Vo where Vo is a constant, as shown in the figure.
Using the separation of variables technique, show that V(x, y) at all points inside the
charge-free square is given by:
V(x, y) =
Σ
4Vo
sin
пп
L
'n#r\sinh(nTy/L)
sinh(nữ)
n=1,3,5,...
Transcribed Image Text:V = 0 y L V = Vo V = 0 L x V = 0 Each side of a square pipe, side length L, is kept fixed at a particular potential, either V = 0 or V = Vo where Vo is a constant, as shown in the figure. Using the separation of variables technique, show that V(x, y) at all points inside the charge-free square is given by: V(x, y) = Σ 4Vo sin пп L 'n#r\sinh(nTy/L) sinh(nữ) n=1,3,5,...
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