Derivation/origin of two equations

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The discussion centers on two equations related to the scattering of electric fields and dipole moments. The first equation describes the amplitude of a scattered electric field, incorporating the dipole moment and the angle between the dipole and line of sight, but lacks clear literature references. The second equation for the scattered dipole moment suggests oscillation in space, raising questions about the nature of dipole oscillation, which is typically time-dependent. The user is seeking clarification on the origins and implications of these equations for their problem. Understanding these equations is crucial for grasping the underlying physics of dipole scattering.
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I've encountered two equations and I'm not sure of their origins. First, there's a differential equation describing the amplitude of a scattered electric field, E=(1/(c^2*r))*dp/dt sin y, where p is the scattered dipole moment and gamma (y) is the angle between the dipole moment and line of sight. The equation makes enough sense, I guess. I'm just not able to find any literature on it or its origin. Also, I'm not sure where the equation for the scattered dipole moment, p=po*exp(-ik(r-ct)), comes from. The r indicates that the dipole is oscillating in space, but if it's a dipole particle it can only oscillate in time, correct?
 
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