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Page 19
... vanishes and the solution is 1 Q ( x ) = √ ̧ p ( x ' ) G2 ( x , x ' ) d3x ' — — f ( x ) - 4πT JS дор da ' Ən ' ( 1.44 ) For Neumann boundary conditions we must be more careful . The obvious choice of boundary condition on G ( x , x ...
... vanishes and the solution is 1 Q ( x ) = √ ̧ p ( x ' ) G2 ( x , x ' ) d3x ' — — f ( x ) - 4πT JS дор da ' Ən ' ( 1.44 ) 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 : 1 y ( x ) = - 4πT S eikR S1 R n • V'y + ik ( 1 + R kR KR / R 灯 yda ' ( 9.65 ) where n is now ...
... vanishes inversely as the hemisphere radius as that radius goes to infinity . Then we obtain the Kirchhoff integral for y ( x ) in region II : 1 y ( x ) = - 4πT S eikR S1 R n • V'y + ik ( 1 + R kR KR / R 灯 yda ' ( 9.65 ) where n is now ...
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 : $ A⋅nda Sv . Ad ( n x S = A ) da = V.A d3x A ...
... 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 : $ A⋅nda Sv . Ad ( n x S = A ) da = V.A d3x A ...
Contents
1 | 1 |
BoundaryValue Problems in Electrostatics I | 26 |
Dielectrics | 98 |
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4-vector Ampère's law angle angular distribution antenna approximation atomic axis B₁ Babinet's principle behavior boundary conditions calculate cavity Chapter charged particle coefficients collisions component conducting conductor consider constant coordinate cross section cylinder d³x dielectric diffraction dimensions dipole direction discussed E₁ electric field electromagnetic fields electrons electrostatic energy loss factor force equation 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 parallel perpendicular phase velocity plane wave plasma polarization power radiated Poynting's vector problem propagation radius region relativistic result S₁ 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