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4-vector acceleration Ampère's law angular distribution approximation atomic axis behavior boundary conditions bremsstrahlung calculation Chapter charge q charged particle Cherenkov radiation classical coefficients collisions component conducting conductor consider constant coordinate cross section cylinder d³x dielectric diffraction dipole direction discussed E₁ electric field electromagnetic fields electron electrostatic emitted energy loss energy transfer equation of motion factor force equation frame frequency given Green's function impact parameter incident particle integral Lagrangian limit Lorentz force Lorentz invariant Lorentz transformation m₁ magnetic field magnetic induction magnitude Maxwell's equations meson modes momentum multipole nonrelativistic obtain orbit oscillations P₁ P₂ parallel perpendicular photon plane plasma polarization power radiated problem quantum quantum-mechanical radius region relativistic result scalar scattering screen shown in Fig shows sin² solid angle solution spectrum sphere spherical surface transverse V₁ vanishes vector potential wave number wavelength ΦΩ