Needs["ErrorBarPlots`"];

data = Import[
   "C:\\Users\\User\\Documents\\DELETE\\Coil_DataWU.csv", "CSV"];

values = ImportString["0	0.37	0.04444	0.002
   0.014	0.36	0.04432	0.002
   0.023	0.35	0.0442	0.002
   0.031	0.32	0.04384	0.002
   0.0343	0.3	0.0436	0.002
   0.0395	0.28	0.04336	0.002
   0.0436	0.27	0.04324	0.002
   0.0469	0.25	0.043	0.002
   0.0501	0.24	0.04288	0.002
   0.0549	0.21	0.04252	0.002
   0.0599	0.19	0.04228	0.002
   0.0667	0.14	0.04168	0.002
   0.0735	0.12	0.04144	0.002
   0.0808	0.11	0.04132	0.002
   0.086	0.09	0.04108	0.002
   0.0912	0.08	0.04096	0.002
   0.097	0.06	0.04072	0.002
   0.1041	0.05	0.0406	0.002
   0.1123	0.04	0.04048	0.002
   0.1203	0.03	0.04036	0.002
   0.1289	0.03	0.04036	0.002
   0.1365	0.02	0.04024	0.002
   0.1408	0.01	0.04012	0.002
   0.156	0.0048	0.0004576	0.002
   0.1625	0.0038	0.0004456	0.002
   0.1716	0.0031	0.0004372	0.002
   0.1783	0.0024	0.0004288	0.002
   0.1878	0.0018	0.0004216	0.002
   0.1975	0.0015	0.000418	0.002
   0.2052	0.0013	0.0004156	0.002
   0.2104	0.0011	0.0004132	0.002
   0.2183	0.0009	0.0004108	0.002
   0.2262	0.0007	0.0004084	0.002
   0.2336	0.0006	0.0004072	0.002
   0.2412	0.0005	0.000406	0.002
   0.2479	0.0004	0.0004048	0.002
   0.254	0.0004	0.0004048	0.002
   0.261	0.0003	0.0004036	0.002
   0.2659	0.0003	0.0004036	0.002
   0.2709	0.0003	0.0004036	0.002
   0.2776	0.0002	0.0004024	0.002
   0.2812	0.0002	0.0004024	0.002
   0.295	0.0002	0.0004024	0.002
   0.3015	0.0001	0.0004012	0.002
   0.3073	0.0001	0.0004012	0.002
   0.3125	0.0001	0.0004012	0.002
   0.3185	0.0001	0.0004012	0.002
   0.3229	0.0001	0.0004012	0.002
   0.3322	0.0001	0.0004012	0.002
   0.341	0	0.0004	0.002"];
mu = 4 e - 7*Pi;
Radius = 0.149;
radius = 0.0582;
frequency = 8313;
field [r_?NumericQ, x_?NumericQ] :=
  mu*frequency*
   Sqrt[2]/(2*Pi*
      Sqrt[x^2 + (Radius + r)^2])*((Radius^2 - x^2 -
         r^2)/(x^2 + (r - Radius)^2)*
      EllipticE[Sqrt[4*r*Radius*(x^2 + (Radius + r)^2)^(-1)]] +
     EllipticK[Sqrt[4*r*Radius*(x^2 + (Radius + r)^2)^(-1)]]);
solution =
  NonlinearModelFit[
   data, (2*i*Pi*Integrate[{field[r, x]}, {r, 0, radius}]), {i}, x];

SetDelayed::write: Tag Times in ((8313 (4 e-7 \[Pi]) ((0.596 EllipticK r Sqrt)/((0.149 +r)^2+x^2)+(0.596 EllipticE r Sqrt (0.022201 -r^2-x^2))/((d^2+(-0.149+r)^2) ((0.149 +r)^2+x^2))))/(\[Pi] ((0.149 +r)^2+x^2)))[r_?NumericQ,x_?NumericQ] is Protected.

FindFit::fitm: Unable to solve for the fit parameters; the design matrix is nonrectangular, non-numerical, or could not be inverted.

FindFit::fitm: Unable to solve for the fit parameters; the design matrix is nonrectangular, non-numerical, or could not be inverted.