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

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Page 82

The study of magnetism began with

electrostatics, the elementary sources were dipoles rather than monopoles, the

basic law of interaction could be considered by introducing hypothetical poles.

The study of magnetism began with

**permanent magnets**. Although, unlike inelectrostatics, the elementary sources were dipoles rather than monopoles, the

basic law of interaction could be considered by introducing hypothetical poles.

Page 90

<$)(mA, - nA,)ds = - J(A x ds), The surface integral in (23) vanishes for a bounded

region of permanent magnetization and so A(r) = J ... Hence in the presence of

...

<$)(mA, - nA,)ds = - J(A x ds), The surface integral in (23) vanishes for a bounded

region of permanent magnetization and so A(r) = J ... Hence in the presence of

**permanent magnets**equation (11) will be modified to „ 4n „ VxB = — j + 47tVx|i or,...

Page 95

c V'M (r') J , ^Mtr^, 0(r) = - f 7^-du' + <j> — ^ds' v J lr - r'l r lr -r'l (31) Of course,

have already seen that we then have fV'xM(rQ , M (Q x ds' A (r) = J du + 0 . w J lr-r'

l r lr ...

c V'M (r') J , ^Mtr^, 0(r) = - f 7^-du' + <j> — ^ds' v J lr - r'l r lr -r'l (31) Of course,

**permanent magnets**may also be dealt with in terms of the vector potential. Wehave already seen that we then have fV'xM(rQ , M (Q x ds' A (r) = J du + 0 . w J lr-r'

l r lr ...

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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