Vector potential and and Intensity of Radiation

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Homework Statement


Let a charge oscillate on a straight line between -a to +a with a frequency ω and according to the law:
κ (x.t) = κ° sin(πx/a) e^(-iωt)
I have to find the following:
1. Vector potential in the dipole approximation
2. Integral of the intensity of radiation

Homework Equations




The Attempt at a Solution


First of all, I tried to calculate the dipole using:
d = ∫ κ (x.t) x dx

After that I calculated vector potential using:
A = 1/(cR) × d(d)/dt
But, I worry that my formula is not correct and I may have used the incorrect formula.

Then I used the formula for calculating the intensity of radiation:

I = (2(second time derivative of dipole)^2) / ( 3c^2)

Please guide me! I have picked up this subject after a long time and things have just jumbled up inside my head.
 

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