Derivation/origin of two equations

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SUMMARY

The discussion centers on two specific equations related to the scattering of electric fields. The first equation, E=(1/(c^2*r))*dp/dt sin y, describes the amplitude of a scattered electric field, where p represents the scattered dipole moment and y is the angle between the dipole moment and the line of sight. The second equation, p=po*exp(-ik(r-ct)), defines the scattered dipole moment, indicating oscillation in space and time. The origin and literature references for these equations are unclear to the participants, highlighting a gap in accessible resources on this topic.

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thewall12
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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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