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Published byGodwin Taylor Modified over 5 years ago

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Dielectric Ellipsoid Section 8

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Dielectric sphere in a uniform external electric field Put the origin at the center of the sphere. Field that would exist without the sphere

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Change in potential caused by sphere Potential of uniform external field Potential outside the sphere

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Solution of Laplace’s Equation in spherical coordinates is of the form Blows up at infinity. Set a = 0. There is no dependence on the azimuthal angle by symmetry The l = 0 term (const/r) doesn’t have the symmetry of the constant vector, the only parameter of the problem. The l = 1 term is the first non-zero term.

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(i) = -B E 0.r Field inside = B E 0, i.e. uniform Inside the sphere, the solution must be finite at the origin. Set b = 0. The l = 0 term is just a constant. Ignore. The l = 1 term is arCos

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Boundary condition on potential

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Normal component of induction is continuous

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Field inside dielectric sphere E (e) is similar to that of a conducting sphere in a uniform field. The sketch is for

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Conducting sphere Dielectric sphere ( (e) = 1)

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