Figure for circular arc of line charge.  One arc of charge on the x-y plane at a fixed radius.  Field point, azimuthal angles for the range of the line charge.

<<peeters` ;
peeters`setGitDir[ "../project/figures/GAelectrodynamics" ]

ClearAll[p1, bold]
pt[r_, t_] := r{Cos[t],Sin[t], 0};
bold = Style[ #, Bold] &;

p1 = Module[{rho, o, x, a, b, e1, e2, e3, rcap,theta, phi},
rho = 1.5;
o = {0,0,0};
x = {1.5,1.8,1.5};
xp = pt[rho, 1.2(a+b)/2];
a= Pi/7;
b = 3 Pi/7;
{e1,e2,e3} = UnitVector[3,#]&/@Range[3];
theta = ArcCos[rcap.e3];
rcap = x // Normalize;
phi = ArcCos[ rcap.e1/Sin[theta]];

Show[
{
ParametricPlot3D[ pt[rho,t], {t, a, b }, PlotRange -> {{-.2,2},{-.2,2},{-.2,2}}, Ticks -> None]/. Line[pts_] :> {Arrowheads[{0,0}],Arrow[Tube[pts,{0.01}]]} ,

ParametricPlot3D[ 0.5{Sin[t]Cos[phi], Sin[t]Sin[phi], Cos[t]}, {t, 0, theta }],

ParametricPlot3D[ pt[rho/6,t], {t, 0,a}],
ParametricPlot3D[ pt[rho/3,t], {t, 0,b}],
Graphics3D[
{
Line[{o, pt[rho,a]}],
Line[{o, pt[rho,b]}],
Red//Darker,
Arrow[{o,x}],
Green//Darker,
Arrow[{o,xp}],
Purple//Darker,
Arrow[{xp,x}],
Blue//Darker,
Arrow[{o,e1}],
Arrow[{o,e2}],
Arrow[{o,e3}],
Black,
Text["a", pt[1.3rho/6,a/2]],
Text["b", pt[1.2rho/3,b/2]],
Text["x'" // bold, xp + Normalize[xp]/10],
Text["x"// bold, x + rcap/10],
Text[Subscript["e"// bold, 1], 1.1 e1],
Text[Subscript["e"// bold, 2], 1.1 e2],
Text[Subscript["e"// bold, 3], 1.1 e3],
Text["θ",
0.6{Sin[t]Cos[phi], Sin[t]Sin[phi], Cos[t]} /. t-> theta/2 ],
}
,BaseStyle->14 
]
}
]
]

rcapPlot[rho_,rcap_]:= Module[{ e1, e2, e3, theta, phi},

{e1,e2,e3} = UnitVector[3,#]&/@Range[3];
theta = ArcCos[rcap.e3];
phi = ArcCos[ rcap.e1/Sin[theta]];

{{theta, phi}/(Pi/2) // N,
ParametricPlot3D[ rho{Sin[t]Cos[phi], Sin[t]Sin[phi], Cos[t]}, {t, 0, theta }, PlotRange -> {{-.2,2},{-.2,2},{-.2,2}}
]
}
]

(*rcapPlot[ 1, {1,1,2}// Normalize]*)

peeters`exportForLatex["lineChargeArcFig1", p1]