Cylindrical.Coord.Laplace.Eq. solution.pdf - Solution to...

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Solution to Laplace’s Equation in Cylindrical Coordinates2,,z112222z2,,z0Use separation of variables:,,zRFHz01R1R1F1222F1H2z2H01R1R12F′′FH′′Hk2TheHzthus satisfies:H′′zk2HzHzCkeikzDkeikzleaving the equation in the form:RddR2k2F′′Fm2TheFthus satisfies:F′′m2FFAmeimBmeimFinally, the equation forRddRm2R2k2R02R′′Rm2R2k2R0Letxik, andRJxand finally one obtains Bessel’s differential equation:x2J′′xJx2m2J0which has two linearly indepent solutions,JxbJmxcNmxThe general solution for,,zis:2,,z0,,zk,meimeikzckmJmik

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Term
Spring
Professor
Unknown
Tags
2 K, Partial differential equation, 0 k, 2 j, 0 j

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