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

Suppose a wire carries a current such taht

I(t) = 0 for t< = 0

= k t for t > 0

Find the electric and magnetic fields generated

2. The attempt at a solution

trying to figure out vector potential first

looking at the diagram

s is the distance fro a point P to the wire which is positioned on the Z axis.

r' is the distance to some section of the wire dz

the only contribution is for t > s/c, otherwise the em fields havent reached the point P

we only need to integrate along the z since there is X and Y symmetry

[tex] z = \pm \sqrt{c^2 t^2 - s^2} [/tex]

but we are going to get the EM fields from time [itex] = t - r' / c = t - \frac{\sqrt{z^2 + s^2}}{c} [/itex]

so we're lookign at integrating this

[tex] A = \frac{\mu_{0}}{4 \pi} 2 \int_{0}^{\sqrt{c^2 t^2 - s^2}} \frac{k (t-\frac{\sqrt{z^2 + s^2}}{c}}{\sqrt{z^2 + s^2}} dz [/tex]

ahve i gone wrong somewhere??

something wrong in my logic?

please help!

thanks for any and all input!

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# Retarded Potentials

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