A linearly polarized plane wave with electric field amplitude E 0 is incident on a small, perfectly

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A linearly polarized plane wave with electric field amplitude Eis 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 kwhere 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 Eand let an origin centered electric dipole field represent the field produced by the sphere. Use this information to deduce that p = 4πϵ0a3Eis the dipole moment induced in the sphere.
(b) Place the sphere in a uniform magnetic field Band 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 kand the scattered wave vector k. If ka

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

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