A linearly polarized plane wave with electric field amplitude E₀ is incident on a small, perfectly conducting sphere. Use the dipole moment information provided in Problem 21.5 and find the angle between the scattering wave vector k and the incident wave vector k₀ where the radiated electric field points in the same direction as E₀.

Data From Problem 21.5

(a) Place a perfectly conducting sphere with radius a in a uniform electric field E₀ and let an origin centered electric dipole field represent the field produced by the sphere. Use this information to deduce that p = 4πϵ₀a³E₀ is the dipole moment induced in the sphere.
(b) Place the sphere in a uniform magnetic field B₀ and let an origin-centered magnetic dipole field represent the field produced by the sphere. Use this information to deduce that m = −(2πa³/μ0)B0 is the dipole moment induced in the sphere.
(c) Let θ be the angle between the incident wave vector k₀ and the scattered wave vector k. If ka

(d) Compare the answer in (c) with the cross section when the incident plane wave is circularly polarized.

Transcribed Image Text:

do dΩ unpol - cose]. 5 =a² (ka)¹ (1 + cos²0) — cos = -