Vs=(p  Cos[θ])/r^2

Es=-Grad[Vs,{r,θ,φ},"Spherical"]

Div[Es,{r,θ,φ},"Spherical"]==0

Vc=TransformedField[ "Spherical"->"Cartesian",Vs,{r,θ,φ}->{x,y,z}]/.p->1

Ec=TransformedField["Spherical"->"Cartesian",Es,{r,θ,φ}->{x,y,z}]/.p->1

equipotentials=ContourPlot3D[Vc,{x,-1,1},{y,-1,1},{z,-1,1}, ContourStyle->Table[{Opacity[.5], Hue[i/10]}, {i,7}], Contours->{-50,-5,-1,0,1,5,50},Mesh->None];

electricField=VectorPlot3D[Ec,{x,-1,1},{y,-1,1},{z,-1,1},VectorScale->{Medium,.5,(3&)}];

Show[equipotentials,electricField]