Question: A point charge q is located at the point (??, ?', z') inside a grounded cylindrical box defined by the surfaces z = 0, z

A point charge q is located at the point (??, ?', z') inside a grounded cylindrical box defined by the surfaces z = 0, z = L, ? = a. Show that the potential inside the box can be expressed in the following alternative forms:

Discuss the relation of the last expansion (with its extra summation) to the other two.

mn Xmnp eim( -4)Jm *.. (, ') %3D XmnL TEnl m -00 n1 Xmmm+1(xmn) sinh X mn Xmn X sinh (L - 2,) sinh 1 . E E elm( - d) sin TE,L sin d(x, x') %3D L. Im L. m=- n=1 . L. Km Im kmz' sin Xmnp kTz X mnP eiml o -6') sin 29 - 2. (7) |-.t. (, ") km Pm+1(Xmn) TELA? Xmn m=-00 k-1 n-1

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