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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: can a positive charge induce negative potential?

    Can a charge, brought into a chargeless world filled with some geometry of conductors and dielectrics, induce a negative potential anywhere in that world? I feel the answer is no. But I cannot think of a good way to prove it, or even attack the problem. More explicitly, imagine a world...
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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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    Induced charge on a conductive shell, potential theory

    There's no electric field inside a conductor, a classic observation of electrostatics. Any field that "should" exist is compensated for by charge redistribution on the surface of the conductor. This produces classic results like shielding since in a hollow conductive shell, the field is still...