Question: (a) Integrate the differential cross sections derived in the text to find the total scattering cross sections and for an infinitely

(a) Integrate the differential cross sections derived in the text to find the total scattering cross sections σ_ΙΙand 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

Eraut(p, 4) = Eo f(k) exp(ikp) P

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

Eraut(p, 4) = Eo f(k) exp(ikp) P

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