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    Electrostatic boundary value problem with radial dielectrics

    Homework Statement A unit sphere at the origin contains no free charge or conductors in its interior or on its boundary. It is, however, embedded in a dielectric medium. The dielectric is linear, but the permitivity varies by angle about the origin. It is constant along any radial direction...
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    Electrostatics: Computing net charge on a specific surface using multiple tests

    Thanks for thinking about this! You're right that it does have some solution if you can analyze all the world's geometry and solve the Laplace equation everywhere, but as you say, this is likely overkill. But that "oracle" I referred to is in fact doing some math magic that actually does do...
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    Electrostatics: Computing net charge on a specific surface using multiple tests

    An interesting electrostatics puzzle! This is a simplification of a real problem I've been hurting my brain on. Luckily the simplification is a fun challenge in its own right. Homework Statement There is a 3D rectangular solid object in space. Each face of the solid is a perfect...
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