## Classical theory of electricity and magnetism: a course of lectures |

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Page 26

Again as the variable parts appear as partial derivatives of 1/r each term

separately is a solution of

shall solve

Again as the variable parts appear as partial derivatives of 1/r each term

separately is a solution of

**Laplace's equation**. Taking the hint from these facts weshall solve

**Laplace's equation**by the separation of variables in spherical polar ...Page 27

As

be a solution so that finally the general solution which is regular everywhere

except at the origin and MULTIPOLE MOMENTS 27 Solution of

As

**Laplace's equation**is linear, the linear combination of such solutions will alsobe a solution so that finally the general solution which is regular everywhere

except at the origin and MULTIPOLE MOMENTS 27 Solution of

**Laplace's****equation**...Page 50

There is another linearly independent solution of Bessel's equation for integral n

but that diverges at x = 0. We write ... Thus the solution of

terms of Bessel functions may be made to satisfy the given boundary conditions.

There is another linearly independent solution of Bessel's equation for integral n

but that diverges at x = 0. We write ... Thus the solution of

**Laplace's equation**interms of Bessel functions may be made to satisfy the given boundary conditions.

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### Contents

The empirical basis of electrostatics | 1 |

Direct calculation of fields | 7 |

dipoles9 The Dirac 5function13 | 13 |

Copyright | |

23 other sections not shown

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acceleration angle angular axis boundary conditions calculate called centre charge density charge distribution charged particle coefficient coil components conducting conductor consider coordinates dielectric constant differential dipole direction distance divergence electric and magnetic electric field electromagnetic field electromotive force electron electrostatic energy flux equation 16 expression field due field point finite fluid formula Fourier frame frequency function given gives Hence incident infinite interaction isotropic Laplace's equation linear Lorentz transformation magnetic field magnitude Maxwell's equations medium molecule momentum motion number density obtain orthogonal oscillations permanent magnets perpendicular photon plane plasma point charge polarization potential due Poynting vector radiation field radiation reaction radius refractive index region relation result satisfied scalar shows sin2 solution special theory sphere at infinity spherical surface integral symmetry tensor term theorem theory of relativity transverse uniform vanishes vector potential velocity volume wave length write zero