(a) Integrate the differential cross sections derived in the text to find the total scattering cross sections σ_ΙΙ and σ_⊥ for an infinitely long and perfectly conducting cylinder with E_inc oriented, respectively, parallel and perpendicular to the cylinder axis.
(b) In two dimensions, the scattering amplitude f(k) = f(k, φ) is defined by the asymptotic electric field

Use the results of part (a) for either polarization to confirm that the optical theorem in two dimensions is

Transcribed Image Text:

Eraut(p, 4) = Eo√ √f(k) exp(ikp) √P