# Vector field of charges

I wanted to plot vector field of 12 positive charges Standing in a circular way with a positive charge at the center all same magnitude. I do not know how to start. Can you please help me Thanks.

• Look up VectorPlot or VectorPlot3D depending on whether it's in the plane or in space. – Michael E2 Oct 3 '19 at 14:40
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• can you upload sketch hand draw of what you mean!? – Alrubaie Oct 3 '19 at 18:04

Electric field lines for 12 negative (left) and 12 positive (right) charges located on a circle

p = Table[{Cos[x], Sin[x], 0}, {x, 0, 2 Pi - Pi/6, Pi/6}];

U[x_, y_, z_] :=
Sum[1/Sqrt[({x, y, z} - p[[i]]).({x, y, z} - p[[i]])], {i, Length[p]}]

Efield = Grad[U[x, y, z], {x, y, z}];

StreamDensityPlot[{Efield[], Efield[]} /. z -> 0.1, {x, -1.5,
1.5}, {y, -1.5, 1.5}, ColorFunction -> "Rainbow",
StreamStyle -> LightGray, StreamPoints -> Fine]

StreamDensityPlot[{-Efield[], -Efield[]} /. z -> 0.05, {x, -1.5,
1.5}, {y, -1.5, 1.5}, ColorFunction -> Hue,
StreamStyle -> LightGray, StreamPoints -> Fine] Electric field lines for 12 negative (left) and 12 positive (right) charges located on a circle + one in the center

p = Table[{Cos[x], Sin[x], 10^-3}, {x, 0, 2 Pi - Pi/6, Pi/6}];

U[x_, y_, z_] :=
Sum[1/Sqrt[({x, y, z} - p[[i]]).({x, y, z} - p[[i]])], {i,
Length[p]}] + 1/Sqrt[{x, y, z}.{x, y, z}]

Efield = Grad[U[x, y, z], {x, y, z}];

StreamDensityPlot[{Efield[], Efield[]} /. z -> 0.1, {x, -1.5,
1.5}, {y, -1.5, 1.5}, ColorFunction -> "Rainbow",
StreamStyle -> LightGray, StreamPoints -> Fine]

StreamDensityPlot[{-Efield[], -Efield[]} /. z -> 0.05, {x, -1.5,
1.5}, {y, -1.5, 1.5}, ColorFunction -> Hue,
StreamStyle -> LightGray, StreamPoints -> Fine] • Many thanks🙏, how is it like when a same charge is placed at the center? – Elahe Lashgari Oct 9 '19 at 7:35
• @ElaheLashgari Do you ask or answer? – Alex Trounev Oct 9 '19 at 11:38
• I asked what if we put a charge with same magnitude and positive right at the center of each circle, how the field looks like then? So imagin we have 13 positive charges instead of 12 – Elahe Lashgari Oct 9 '19 at 12:53
• @ElaheLashgari See update to my answer. – Alex Trounev Oct 9 '19 at 15:43
• Thanks, just a question, what does this line mean? What is P[[i]] here?Sum[1/Sqrt[({x, y, z} - p[[i]]).({x, y, z} - p[[i]])], {i, Length[p]}] + 1/Sqrt[{x, y, z}.{x, y, z} – Elahe Lashgari Oct 11 '19 at 6:01

This is beginning you can do the rest!

or = Graphics[{PointSize[Large], Point[{0, 0}]}];
g1 = ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 2 Pi}];
pp = Table[{Cos[t], Sin[t]}, {t, 0, 2 Pi, Pi/6}];
g2 = ListPlot[pp, PlotStyle -> {Black, PointSize[Large]}];
Show[g1, g2, or] • Great,many Thanks it is a big help🙏 – Elahe Lashgari Oct 7 '19 at 5:41
• This is exactly what I wanted to plot it’s electric field vector. Can you please help me with that. – Elahe Lashgari Oct 8 '19 at 3:17