## Classical Electrodynamics |

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Page 16

We want to show the uniqueness of the

47p, inside a volume V subject to either Dirichlet or Neumann boundary

conditions on the closed bounding surface S. We suppose, to the contrary, that

there exist ...

We want to show the uniqueness of the

**solution**of Poisson's equation, V*q = —47p, inside a volume V subject to either Dirichlet or Neumann boundary

conditions on the closed bounding surface S. We suppose, to the contrary, that

there exist ...

Page 17

Dirichlet Open surface Not enough Not enough Unique, stable

direction Closed surface Unique, stable Too much Too much

Open surface Not enough Not enough Unique, stable

Dirichlet Open surface Not enough Not enough Unique, stable

**solution**in onedirection Closed surface Unique, stable Too much Too much

**solution**NeumannOpen surface Not enough Not enough Unique, stable

**solution**in one direction ...Page 81

Whereas the expansion for a single sphere is most easily obtained from the

image

obtain by the method of images, since it involves an infinite set of images.

Whereas the expansion for a single sphere is most easily obtained from the

image

**solution**, the general result (3.125) for a spherical shell is rather difficult toobtain by the method of images, since it involves an infinite set of images.

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### Contents

Introduction to Electrostatics | 1 |

Nš 3 | 3 |

Greens theorem | 14 |

Copyright | |

30 other sections not shown

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### Common terms and phrases

angle angular applied approximation assumed atomic average axis becomes boundary conditions calculate called Chapter charge classical collisions compared component conducting conductor Consequently consider constant coordinates cross section cylinder defined density depends derivative determine dielectric dimensions dipole direction discussed distance distribution effects electric field electromagnetic electron electrostatic energy equal equation example expansion expression factor force frame frequency function given gives incident inside integral involved limit Lorentz loss magnetic magnetic field magnetic induction magnitude mass means momentum motion moving multipole normal observation obtain origin parallel particle physical plane plasma polarization position potential problem properties radiation radius region relation relative result satisfy scalar scattering shows side simple solution space sphere spherical surface transformation unit vanishes vector velocity volume wave written