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Mathematics Homework Solutions
#28506
Electrostatic Potential
In this problem, you will find the electrostatic potential inside an infinitely long, grounded, metal cylinder of unit radius whose axis coincides with the z-axis (See figure below). In cylindrical coordinates, the potential, V(r, theta, z), satisfies Laplace's equation... Please see attached... Let us assume that the potential is known at z = 0, so that
V(r, theta, z)= f(r, theta)
is a given function.
Because of the symmetry in the problem, V(r, theta, -z) = V(r, theta, z), so we only have to consider the semi-infinite cylinder in the domain z>0. Since the cylinder is grounded, the potential there must be zero, meaning that V(1, theta, z) = 0...
Please see attached for full question.
The 6 pages solution shows how to solve Lapalace equation in cylindrical coordinates and how to apply the boundary conditions.
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