## Classical electrodynamics |

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Page 3

At this point it is worth while to introduce the Dirac

dimension, the

function having the properties : (1) d(x — a) = 0 for x =£ a, and (2) I 5(x — a) dx =

1 if the ...

At this point it is worth while to introduce the Dirac

**delta function**. In onedimension, the

**delta function**, written d(x — a), is a mathematically improperfunction having the properties : (1) d(x — a) = 0 for x =£ a, and (2) I 5(x — a) dx =

1 if the ...

Page 4

From the definitions above it is evident that, for an arbitrary function /(#), (3) f /(a;)

d(x -a)dx = f(a), and (4) f /(*) <5'(* -a)dx = -f'(a), where a prime denotes

differentiation with respect to the argument. If the

a function ...

From the definitions above it is evident that, for an arbitrary function /(#), (3) f /(a;)

d(x -a)dx = f(a), and (4) f /(*) <5'(* -a)dx = -f'(a), where a prime denotes

differentiation with respect to the argument. If the

**delta function**has as argumenta function ...

Page 37

... and d(r — r,-) is the radial

unchanged. Consequently we have The radial

according to rule 5 at the end of Section 1.2 as a* * r» / a*\ a\l a* \ -- r,.| = -2<5|r ...

... and d(r — r,-) is the radial

**delta function**.* Under inversion the angular factor isunchanged. Consequently we have The radial

**delta function**can be transformedaccording to rule 5 at the end of Section 1.2 as a* * r» / a*\ a\l a* \ -- r,.| = -2<5|r ...

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### Contents

Introduction to Electrostatics | 1 |

Scalar potential | 7 |

Greens theorem | 14 |

Copyright | |

17 other sections not shown

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### Common terms and phrases

4-vector acceleration angular distribution approximation assumed atomic average axis behavior Bessel functions boundary conditions bremsstrahlung calculate Chapter charge density charge q charged particle classical coefficients collisions component conductor Consequently consider coordinates cross section current density cylinder defined delta function dielectric constant diffraction dimensions dipole direction discussed effects electric field electromagnetic fields electron electrostatic emitted energy loss expansion expression factor force equation frequency given Green's function impact parameter incident particle inside integral Laplace's equation limit linear Lorentz invariant Lorentz transformation macroscopic magnetic field magnetic induction magnitude Maxwell's equations meson molecules momentum multipole multipole expansion nonrelativistic obtain orbit oscillations parallel perpendicular photon plane wave plasma point charge polarization power radiated problem quantum quantum-mechanical radiative radius region relativistic result scalar scattering shown in Fig shows solid angle solution spectrum spherical surface theorem transverse vanishes vector potential wave equation wave number wavelength written zero