In[171]:= Needs["ErrorBarPlots`"];

data = Import[
   "C:\\Users\\User\\Documents\\DELETE\\Coil_DataWU.csv", "CSV"];
data = data /. s_String :> ToExpression[s]

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_?NumericQ, Radius_?NumericQ,
   frequency_?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 =
  FindFit[data,
   2*i*Pi*Integrate[{field[r, x, mu, Radius, frequency]}, {r, 0,
      radius}], {{i, .7}}, x];

Out[173]= {{0, 0.37}, {0.014, 0.36}, {0.023, 0.35}, {0.031,
  0.32}, {0.0343, 0.3}, {0.0395, 0.28}, {0.0436, 0.27}, {0.0469,
  0.25}, {0.0501, 0.24}, {0.0549, 0.21}, {0.0599, 0.19}, {0.0667,
  0.14}, {0.0735, 0.12}, {0.0808, 0.11}, {0.086, 0.09}, {0.0912,
  0.08}, {0.097, 0.06}, {0.1041, 0.05}, {0.1123, 0.04}, {0.1203,
  0.03}, {0.1289, 0.03}, {0.1365, 0.02}, {0.1408, 0.01}, {0.156,
  0.0048}, {0.1625, 0.0038}, {0.1716, 0.0031}, {0.1783,
  0.0024}, {0.1878, 0.0018}, {0.1975, 0.0015}, {0.2052,
  0.0013}, {0.2104, 0.0011}, {0.2183, 0.0009}, {0.2262,
  0.0007}, {0.2336, 0.0006}, {0.2412, 0.0005}, {0.2479,
  0.0004}, {0.254, 0.0004}, {0.261, 0.0003}, {0.2659,
  0.0003}, {0.2709, 0.0003}, {0.2776, 0.0002}, {0.2812,
  0.0002}, {0.295, 0.0002}, {0.3015, 0.0001}, {0.3073,
  0.0001}, {0.3125, 0.0001}, {0.3185, 0.0001}, {0.3229,
  0.0001}, {0.3322, 0.0001}, {0.341, 0}}

During evaluation of In[171]:= FindFit::fitm: Unable to solve for the fit parameters; the design matrix is nonrectangular, non-numerical, or could not be inverted.

During evaluation of In[171]:= FindFit::fitm: Unable to solve for the fit parameters; the design matrix is nonrectangular, non-numerical, or could not be inverted.