Separation of Variables: Cartesian coordinates A rectangular metal tube (its height extends from z = 0 to infinity) is placed on the xy plane. See Fig. 1. The side faces of the tube are kept at zero potential, V = 0, and the face of the base, supported on the xy plane, is maintained at a potential Vo (x.y). a) Calculate the potential inside the tube. b)Assume that the base plate, the one that rests on the xy plane, is conductive and maintained at constant potential, that is,Vo (x,y) = V.Calculate the potential inside the tube and determine the density of load o (x, y) on this plate, at z = 0. It might be useful know that: σ = - εo ∂V / ∂n

Separation of Variables: Cartesian coordinates A rectangular metal tube (its height extends from z = 0 to infinity) is placed on the xy plane. See Fig. 1. The side faces of the tube are kept at zero potential, V = 0, and the face of the base, supported on the xy plane, is maintained at a potential Vo (x.y). a) Calculate the potential inside the tube. b)Assume that the base plate, the one that rests on the xy plane, is conductive and maintained at constant potential, that is,Vo (x,y) = V.Calculate the potential inside the tube and determine the density of load o (x, y) on this plate, at z = 0. It might be useful know that: σ = - εo ∂V / ∂n

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Question

Separation of Variables: Cartesian coordinates A rectangular metal tube (its height extends from z = 0 to infinity) is placed on the xy plane. See Fig. 1. The side faces of the tube are kept at zero potential, V = 0, and the face of the base, supported on the xy plane, is maintained at a potential Vo (x.y). a) Calculate the potential inside the tube.
b)Assume that the base plate, the one that rests on the xy plane, is conductive and maintained at constant potential, that is,Vo (x,y) = V.Calculate the potential inside the tube and determine the density of load o (x, y) on this plate, at z = 0. It might be useful know that: σ = - εo ∂V / ∂n