Quiet@Remove["Global`*"];
$HistoryLength=2;
SetDirectory[NotebookDirectory[]];
Needs["VectorAnalysis`"]
SetCoordinates[Cylindrical[r,fi,z]];

hacko={0,0,Hz[r]};
ecko={0,Efi[r],0};
becko=μ*hacko;
rce1=Thread[Curl[ecko]==-I*ω*becko][[3]]
rce2=Thread[Curl[hacko]==γ*ecko][[2]]

(DSolve[{rce1,rce2},{Hz[r],Efi[r]},r]//Simplify[#,{r>0,μ>0,ω>0}]&)/.C[2]->0

rmax=0.04;
protisk=((BesselJ[0,(((-1))^(3/4)) r (Sqrt[γ μ ω])])/(BesselJ[0,(((-1))^(3/4)) rmax (Sqrt[γ μ ω])]))/.{γ->57*(10^6),μ->4.*Pi*(10^(-7)),ω->314}
Plot[Abs[protisk],{r,0,rmax},PlotRange->All,AxesOrigin->{0,0}]

(Sqrt[(2/(ω*γ*μ))])/.{γ->57*(10^6),μ->4.*Pi*(10^(-7)),ω->314}

(100/0.7)