Classical Electrodynamics |
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Page 57
... obtain a compact representation of the Legendre polynomials , known as Rodrigues ' formula : P1 ( x ) = 1 d ' 2'1 ! dx1 ( x2 - 1 ) 2 ( 3.16 ) [ This can be obtained by other , more elegant means , or by direct l - fold integration of ...
... obtain a compact representation of the Legendre polynomials , known as Rodrigues ' formula : P1 ( x ) = 1 d ' 2'1 ! dx1 ( x2 - 1 ) 2 ( 3.16 ) [ This can be obtained by other , more elegant means , or by direct l - fold integration of ...
Page 86
... obtained from this expansion . If we let x ' → 0 , only the m = 0 term survives , and we obtain the integral representation : 1 2 00 cos kz Ko ( kp ) dk √ p2 + z2 = - T30 · ( 3.150 ) If we replace p2 in ( 3.150 ) by R2 = p2 + p'2 ...
... obtained from this expansion . If we let x ' → 0 , only the m = 0 term survives , and we obtain the integral representation : 1 2 00 cos kz Ko ( kp ) dk √ p2 + z2 = - T30 · ( 3.150 ) If we replace p2 in ( 3.150 ) by R2 = p2 + p'2 ...
Page 96
... Obtain the following expansion : 1 x - x ' = Σ m = So 0 dk eim ( - ) Jm ( kp ) Jm ( kp' ́ ) e - k ( ≈ > - * < ) ( c ) By appropriate limiting procedures prove the following expansions : 2 1 + 22 = 0 Jo ( kVp + p2 - 2pp ' cos $ ) eikp ...
... Obtain the following expansion : 1 x - x ' = Σ m = So 0 dk eim ( - ) Jm ( kp ) Jm ( kp' ́ ) e - k ( ≈ > - * < ) ( c ) By appropriate limiting procedures prove the following expansions : 2 1 + 22 = 0 Jo ( kVp + p2 - 2pp ' cos $ ) eikp ...
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