 Electric-dipole radar cross section of a small conducting sphere

Retaining only the electric dipole induced in a small sphere gives $\mathbf{p}=4\pi {ϵ}_0{a}^3{\mathbf{E}}_{\mathrm{inc}}$. In the backward direction its differential scattering cross-section is $k^4{a}^6$, so the radar cross section is $4\pi k^4{a}^6$. This response model omits the sphere's induced magnetic dipole moment; it must be distinguished from perfect-conductor sphere dipole interference.