3322.sagews

epsilon=.1
q=1
comp=.1
k=(1/(4*pi*epsilon))
V(x,y)=(1/sqrt(x^2+y^2+comp))

vp=plot_vector_field((V(x+1,y)+V(x-1,y)).gradient(), (x,-2,2), (y,-2,2), color='blue')
cp=contour_plot((V(x+1,y)+V(x-1,y)).gradient().norm(), (x,-2,2), (y,-2,2),contours=(3,2.5,2,1.5,1),fill=false)
(cp+vp).show()

vp=plot_vector_field((-V(x+1,y)+V(x-1,y)).gradient(), (x,-2,2), (y,-2,2), color='blue')
cp=contour_plot((-V(x+1,y)+V(x-1,y)).gradient().norm(), (x,-2,2), (y,-2,2),contours=(.5,2,.1,1,1.5),fill=false)
(cp+vp).show()

vp=plot_vector_field((-V(x+1,y)+(2*V(x-1,y))).gradient(), (x,-3,3), (y,-3,3), color='blue')
cp=contour_plot((-V(x+1,y)+(2*V(x-1,y))).gradient().norm(), (x,-3,3), (y,-3,3),contours=(3,2,1,.5,.1),fill=false)
(cp+vp).show()

vp=plot_vector_field((-V(x+1,y)+(2*V(x-1,y))).gradient(), (x,-10,10), (y,-10,10), color='blue')
cp=contour_plot((-V(x+1,y)+(2*V(x-1,y))).gradient().norm(), (x,-10,10), (y,-10,10),contours=(3,2,1,.5,.1),fill=false)
(cp+vp).show()