Scattering 1 Classical scattering of a charged particle (Rutherford ...

E ≈ E 0 e iω(t−z/c) iω(n − 1)∆z[1 − c ]Divide through by the thickness ∆z and identify this result with the previous calculation ofthe scattered field;(n − 1) = 2πq2 (N/∆z)4πǫm(ω 2 0 − ω2 )The term N/∆z is the Number density of the electrons.11 Cherenkov RadiationCherenkov radiation occurs when a charged particle is moving faster that EM radiation travelsin that medium. Observe figure 8. The present point lies a further distance from theretarded point than the observation point. That is V (t − t ′ ) > (c/n)(t − t ′ ). Here, n is theindex of refraction of the medium. A wave front can be drawn as a line that lies from thetangent to the spherical wave front to the present point as shown in fig. 8. Each sphericalwave front from a point along the particle trajectory will be tangent to this line. The angleof propagation of the wave front θ is obtained from the figure as;(c/n)tθFigure 8: The geometry of wave fronts in Chernekov radiationvtcos(θ) = ct/nvt= 1nβPreviously we chose the retarded point of the Lienard-Eiechert potentials because of causality.In Cherenkov radiation both retarded and advanced points are possible solutions as onecan see in fig. 9 The positions of the observation and present points are related by (we usec here but note that it is really c/n);c(t − t ′ ) = | ⃗ X + ⃗ V (t − t ′ )| = R/c16