Classical Electrodynamics |
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Page 19
... vanishes and the solution is • ( x ) = √2 p € p ( x ' ) G ( x , x ' ) ď3x ' - p ( x ' ) GƊ ( x , x ' ) d3x ' 4π JS 18 0 ( x ) 3Gp da ' ( 1.44 ) Ən ' For Neumann boundary conditions we must be more careful . The obvious choice of ...
... vanishes and the solution is • ( x ) = √2 p € p ( x ' ) G ( x , x ' ) ď3x ' - p ( x ' ) GƊ ( x , x ' ) d3x ' 4π JS 18 0 ( x ) 3Gp da ' ( 1.44 ) Ən ' For Neumann boundary conditions we must be more careful . The obvious choice of ...
Page 282
... vanishes inversely as the hemisphere radius as that radius goes to infinity . Then we obtain the Kirchhoff integral for y ( x ) in region II : eik R i y ( x ) = 4 SR n . [ V'w + ik ( 1 + 1 ) Ry ] da ( 9.65 ) 1 4πT KR / R yda ' where n ...
... vanishes inversely as the hemisphere radius as that radius goes to infinity . Then we obtain the Kirchhoff integral for y ( x ) in region II : eik R i y ( x ) = 4 SR n . [ V'w + ik ( 1 + 1 ) Ry ] da ( 9.65 ) 1 4πT KR / R yda ' where n ...
Page 284
... vanishes identically . To do this we make use of the following easily proved identities connecting surface integrals over a closed surface S to volume integrals over the interior of S : & S A⚫n da = V. A d3x § ( n x A ) da = √ √ x ...
... vanishes identically . To do this we make use of the following easily proved identities connecting surface integrals over a closed surface S to volume integrals over the interior of S : & S A⚫n da = V. A d3x § ( n x A ) da = √ √ x ...
Common terms and phrases
4-vector acceleration Ampère's law angle angular distribution antenna approximation atomic axis Babinet's principle behavior boundary conditions calculate cavity Chapter charge q charged particle coefficients collisions component conducting conductor constant coordinate cross section cylinder d³x dielectric dielectric constant diffraction dipole direction discussed E₁ electric field electromagnetic fields electron electrostatic energy loss factor force equation frame frequency given Green's function impact parameter incident particle integral Kirchhoff Lagrangian Laplace's equation Lorentz force Lorentz invariant Lorentz transformation m₁ magnetic field magnetic induction magnitude Maxwell's equations meson modes momentum multipole nonrelativistic obtain oscillations P₁ P₂ parallel perpendicular phase velocity plane wave plasma polarization power radiated problem propagation radius region relativistic result scalar scattering screen shown in Fig shows sin² solution sphere spherical surface transverse unit V₁ vanishes vector potential velocity wave guide wave number wavelength ΦΩ