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Radiation from a Moving Charged Particle

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Classical Relativistic Electrodynamics

Part of the book series: Advanced Texts in Physics ((ADTP))

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Abstract

We consider an inhomogeneous wave equation of the same form as treated in Sect. 1.9,

$${\nabla ^2}\psi - \frac{2}{{{u^2}}}\frac{{{\partial ^2}\psi }}{{\partial {t^2}}} = - f\left( {r,t} \right)$$
(3.1.1)

where Ψ corresponds to a scalar potential Ø or any component of a vector potential A,f a source producing the field Ψ, and u the speed of light in an unbounded non-dispersive medium with permittivity ε and permeability µ. In order to solve the inhomogeneous wave equation in an unbounded region, we will try to find a time-dependent Green function corresponding to (3.1.1), which satisfies an inhomogeneous wave equation

$$\left( {{\nabla ^2} - \frac{1}{{{u^2}}}\frac{{{\partial ^2}}}{{\partial {t^2}}}} \right)G\left( {r,t;r',t'} \right) = - \delta \left( {r - r'} \right)\delta \left( {t - t'} \right).$$
(3.1.2)

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© 2004 Springer-Verlag Berlin Heidelberg

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Shiozawa, T. (2004). Radiation from a Moving Charged Particle. In: Classical Relativistic Electrodynamics. Advanced Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06261-6_3

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  • DOI: https://doi.org/10.1007/978-3-662-06261-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05834-9

  • Online ISBN: 978-3-662-06261-6

  • eBook Packages: Springer Book Archive

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