(* Plotting field lines for E = 1/r^3 (2 Cos[theta] r-hat + Sin[theta] theta-hat),
in the y-z plane (x = 0 and phi = 90 deg), with r-hat and theta-hat being put in terms of y-hat and z-hat so I can have the components of E for use in the StreamPlot command *)
(* To be specific, I said that:
r = (y^2 + z^2)^1/2
theta = angle from z-axis, see below
r-hat = sin(theta) y-hat + cos(theta) z-hat
theta-hat = cos(theta) y-hat - sin(theta) z-hat
 *)
(* then I grouped all the y-hat terms together and all the z-hat terms together *)
theta[y_,z_]=ArcTan[z,y];  (* using arctan function with 2 arguments gets rid of the problem with quadrants 2 and 3 *)
StreamPlot[{(y^2+z^2)^(-3/2) 3 Cos[theta[y,z]] Sin[theta[y,z]], (y^2+z^2)^(-3/2) ( 2(Cos[theta[y,z]])^2 - (Sin[theta[y,z]])^2 )},{y,-10,10},{z,-10,10}]