## Classical electrodynamics |

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Page 296

The power radiated per unit solid angle in the scalar Kirchhoff

dP — dQ. D (fca)2 P< — _ cos a 477 /cos a + cos 0\2 \ 2 cos a / (9.112) where /*<

is given by (9.104). If we compare the vector Kirchhoff result (9.103) with (9.112),

...

The power radiated per unit solid angle in the scalar Kirchhoff

**approximation**isdP — dQ. D (fca)2 P< — _ cos a 477 /cos a + cos 0\2 \ 2 cos a / (9.112) where /*<

is given by (9.104). If we compare the vector Kirchhoff result (9.103) with (9.112),

...

Page 297

Then both scalar and vector

dP ^ ... There is reason to believe that the vector Kirchhoff result is close to the

correct one, even though the

Then both scalar and vector

**approximations**reduce to the common expression,dP ^ ... There is reason to believe that the vector Kirchhoff result is close to the

correct one, even though the

**approximation**breaks down seriously for ka < 1.Page 307

(b) Compare your result in part (a) with the standard scalar Kirchhoff

plane of incidence. 9.8 A rectangular opening with sides of length a and b > a

defined by x ...

(b) Compare your result in part (a) with the standard scalar Kirchhoff

**approximation**and with the result in Section 9.8 for the polarization vector in theplane of incidence. 9.8 A rectangular opening with sides of length a and b > a

defined by x ...

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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