![W[( x )] = 1/(x^2 + y^2) ( -y ) y x z 0](../HTMLFiles/Lect3_234.gif)
swirls around cylinders centered on the 
-axis.
3D
Magnetic Field or Winding
swirls around cylinders centered on the -axis.
![[Graphics:../HTMLFiles/Lect3_236.gif]](../HTMLFiles/Lect3_236.gif)
Click to open a live view of "swirl around cylinders"
Inverse Square Law
![G[X] = 1/(| X |^2) · 1/(| X |) X = 1/ρ^2R](../HTMLFiles/Lect3_237.gif){kind=small}
, has zero divergence, 
, except at the origin where it is undefined.
![[Graphics:../HTMLFiles/Lect3_239.gif]](../HTMLFiles/Lect3_239.gif)
Torus Invariant
![T[x, y, z] = 1/((x^2 + y^2) (((x^2 + y^2)^(1/2) - R)^2 + z^2)) ( 2 2 ... (-R + Sqrt[x + y ]) z](../HTMLFiles/Lect3_240.gif)
⇔ ![T[ρ, θ, ϕ] = 1/(ρ (R + ρ Cos[ϕ])) ( Cos[θ] Cos[b ... Sin[θ] Sin[ϕ]](../HTMLFiles/Lect3_241.gif)
![[Graphics:../HTMLFiles/Lect3_242.gif]](../HTMLFiles/Lect3_242.gif)
Created by Mathematica (July 2, 2004)