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Page 19
... vanishes and the solution is Q ( x ) = [ _ p ( x ' ) G2 ( x , x ' ) d3x ' - 1 § . ∞ ( x ) Gp da D ( X ) ( 1.44 ) 4πT JS For Neumann boundary conditions we must be more careful . The obvious choice of boundary condition on G ( x , x ...
... vanishes and the solution is Q ( x ) = [ _ p ( x ' ) G2 ( x , x ' ) d3x ' - 1 § . ∞ ( x ) Gp da D ( X ) ( 1.44 ) 4πT JS For Neumann boundary conditions we must be more careful . The obvious choice of boundary condition on G ( x , x ...
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 : y ( x ) = - 1 4πT S ik R n . V'y + ik 1 + S1 R iR KR / R Y da ' ( 9.65 ) where n is now a ...
... vanishes inversely as the hemisphere radius as that radius goes to infinity . Then we obtain the Kirchhoff integral for y ( x ) in region II : y ( x ) = - 1 4πT S ik R n . V'y + ik 1 + S1 R iR KR / R Y da ' ( 9.65 ) where n is now a ...
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 V f √ ( n × A ) da ...
... 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 V f √ ( n × A ) da ...
Contents
1 | 1 |
BoundaryValue Problems in Electrostatics I | 26 |
Dielectrics | 98 |
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4-vector acceleration Ampère's law angular distribution antenna approximation atomic axis B₁ Babinet's principle behavior boundary conditions calculate Chapter charge q charged particle coefficients collisions component conducting conductor consider constant coordinate cross section cylinder d³x dielectric diffraction dipole direction discussed E₁ electric field electromagnetic fields electron electrostatic energy loss energy transfer 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 momentum multipole nonrelativistic obtain oscillations P₁ P₂ parallel perpendicular phase velocity plane wave plasma polarization power radiated problem radius region relativistic result S₁ scalar scattering screen shown in Fig shows sin² solid angle solution sphere spherical surface transverse unit V₁ vanishes vector potential velocity wave number wavelength ΦΩ