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A charged particle moves along the y axis according to the law y = a cos ωt, and the point of observation P is located on the x axis at a distance l from the particle (l >> a). Find the ratio of electromagnetic radiation flow densities S1/S2 at the point P at the moments when the coordinate of the particle y1 = 0 and y2 = a. Calculate that ratio if ω = 3.3.106 s-1 and l = 190 m.

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P is a fixed point at a distance l from the equilibrium position of the particle. Because l > a, to first order in a/l the distance between P and the instantaneous position of the particle is still l. For the first case y = 0 so t = T/4

The corresponding retarded time is 

For the second case y = a at t = 0 so at the retarded time 

The radiation fluxes in the two cases are proportional to 

Note : The radiation received at P at time t depends on the acceleration of the charge at the retarded time.

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