This is what I am writing::: START at the point y=0, just at the ring’s edge, where we say r=k.  Here,  on the outside axis,  r^2 = x^2 -1.  .  Since the E-fields are in Kerr coords, we differentiate wrt /x,y/ :  dE = ∂E/∂r ∂r/dx + ∂E/∂theta ∂theta/dx… for both components, /x,y/ separately; also we process both field components, at least with increasing ‘y’.   At the starting edge point, the sqrt gives  r= sqrt(x^2 – 1) , and with   k^2 = [x_0^2]  – 1 ,  we can write   ‘x’_0 as  sqrt[ 1 + k^2 ] ≈ 1 + 1/2 k^2 .  OK, this is the RING POINT, my TINKER BELL POINT. Now I expand the two field components, around THIS POINT.
I think Steve will see this process yielding my TINKER BELL EQUATIONS.
Moving a bit in the equatorial plane with a ‘dx’, clearly only the radial part changes. Moving with a ‘dy’ is more subtle.



One thought on “FULL COORD PRESS

  1. ‘It looks like the dang theta-field gets stronger faster, I’ll be… I mean, not in dx clearly, but whoa, as you have shown !! It gets stronger in dy than the radial field does, even in dx. AWRIIIIIIIIIIIIIIGHT.
    This is tricky stuff, and I am enjoying beers on this last ‘hot’ day
    of summer, but hey, low 90’s with dry air is HAPPY GARDEN camp
    It’s “pretty much” 1/r^2, vs. 1/r, see ??………
    Works out when you have a min. ‘r’…I always generate enought stuff that I boggle, tho I think I have it. Basically, tho I will assemble it all, the cosine does not rapidly change in Kerr, with dx, dy at the edge. AWRIIIIIIIIIIIIIIIIIIIGHT.ALL, as you have gloriously depicted, at a pretty stoooopidly small scale. BEEEERS.


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