(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculate the magnetic vector potentialAat a point p located at a distance r from the axis of an oscillating dipole of length s.

It is assumed that [tex]r\gg s[/tex] and that the current is the same throughout s.

2. Relevant equations

[tex]r=\sqrt{(x^2+(z-z')^2)},[/tex] where x,z is the horizontal and vertical coordinates of p, respectively, and z' is the vertical coordinate of the source point. The axis of the dipole lies on the z axis, and so x'=0. The problem is confined to the xz plane only.

[tex]A=c\int^{s/2}_{-s/2}\frac{\exp(ikr)}{r}dz' \hat{z},[/tex]

where c is a constant and [tex]k[/tex] is the wave number. The exponential comes from the fact that the current is a function of the retarded time, [tex][t]=t-r/c[/tex].

3. The attempt at a solution

I really don't know how to calculate this integral. Without the exponential I would've been fine, but now... lol wut? Are there perhaps some approximations, expansions, or variable changes that I could do? Any tips?

If it is of any help, the answer is apparently the same answer as in the case of a current localized at the center of the dipole:

[tex]A=d*\frac{\exp(i\omega[t])}{r}s \hat{z}[/tex]

(d is a constant.)

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# Homework Help: Vector potential due to oscillating dipole

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