I have two functions $f(r,\phi)$, and $g(r,\phi)$.
What is the best way to find the curve in the plane $(x,y)$ or $(r,\phi)$, over which $f(r,\phi)=g(r,\phi)$?
I know how to plot it, using
ContourPlot, but it seems that both
FindRoot aren't suited to solve my problem. Any help?
My functions are:
Q00=1; a=1; k=0.01; dQ1[r_, ϕ_] = Q00/2 (BesselK[0, k r]/BesselK[0, k a] + BesselK[1, k r]/BesselK[1, k a] Cos[ϕ]); f[r_, ϕ_] := -(Q00/2) + dQ1[r, ϕ]; g[r_, ϕ_] = Q00 /2 Sin[ϕ] (a/r);
The range I am interested in is $a<r<L$, with $L=10$, and $0\leq\phi\leq 2\pi$