# How to graph power law normalized for specific parameters?

I'm trying to plot the type-II superconductors power law for different values of its parameters. I'm currently using the next code. But I want specific values for n, not an iteration, for example, n=1,3,5,15,25,50. Also I want to plot as: J/J0 vs E/E0, but can't manage to do it. I know it's kinda silly, but I can't find a way of doing it, having a little trouble with ":=" and "=" for plotting functions. Thanks in advance!

E0 = 4*10^-4;
J0 = 1*10^3;
Elec[n_] := E0 (J/J0)^n

Plot[Evaluate@Table[Elec[n], {n, 1, 25, 4}], {J, 0, J0},
PlotRange -> All,
PlotLegends -> {"n=1", "n=5", "n=9", "n=13", "n=17", "n=21"},
PlotStyle -> {Thick}, Frame -> True, GridLines -> Automatic]


An example of the graph i'm looking: • Instead of {n, 1, 25, 4}, you can write a list over which to iterate {n, {1, 3, 5, 15, 25, 50}} – MarcoB May 25 '20 at 0:58
• Thank you! Did not thought of that solution haha. – Santiago G. May 25 '20 at 2:15

## 1 Answer

Here is something closer to your desired result (using your definitions):

ParametricPlot[
Evaluate@Table[{J/J0, Elec[n]/E0}, {n, {1, 5, 9, 13, 17, 21}}],
{J, 0, J0},

(*AspectRatio to reproduce the ratio in your plot, and in Plot *)
AspectRatio -> 1/GoldenRatio,

(* adjust plot range, and prevent dots from being clipped*)
PlotRange -> All, PlotRangePadding -> 0, PlotRangeClipping -> False,
PlotLegends -> {"n = 1", "n = 5", "n = 9", "n = 13", "n = 17", "n = 21"},
PlotStyle -> Thick, Frame -> True, GridLines -> Automatic,
(*MaxRecursion -> 0 turns off the adaptive sampling features, *)
(*giving equally spaced mesh points*)
MaxRecursion -> 0,

(*Mesh -> All shows all the points used in the plotting*)
Mesh -> All, MeshStyle -> PointSize[0.015]
FrameLabel -> (Style[#, 14, Black] & /@
{"J/\!$$\*SubscriptBox[\(J$$, $$0$$]\)",
"E/\!$$\*SubscriptBox[\(E$$, $$0$$]\)"})
] • wow! Thanks a lot! Looks great. Also thanks for commenting the code. – Santiago G. May 26 '20 at 16:48
• @Santiago You are very welcome! – MarcoB May 26 '20 at 17:13