How to plot fields inside round wire REVIEWED

How to plot the transverse electric field in a round wire PhL 12.12.13 This never got much off the ground. I proposed the reader do it at the end of Appendix D. I have not done this, but I think this is how you could do it. First, pick z = 0. Then I think we have Etransverse(r,φ) = cos(-ωt+mφ + arg[Eφ(r)] ) |Eφ| + cos(-ωt +mφ + arg[Er(r)] ) |Er| Then use e'1 = cosφ e1 + sinφ e2 e'2 = - sinφ e1 + cosφ e2 Proof #1: to replace = -sinφ + cosφ = cosφ + sinφ and then you have Etransverse(r,φ) = cos(-ωt + mφ + arg[Eφ(r)] ) |Eφ| [-sinφ + cosφ ] + cos(-ωt + mφ + arg[Er(r)] ) |Er| [cosφ + sinφ ] and then given the complex expressions for Er(r,m) and Eφ(r,m), you could plot the actual physical transverse electric field vector Etransverse(r,φ) at this instant in time. This is for z = 0. The vector's direction and magnitude will change with t in a complicated way. Ah, but for fixed r and φ this has the form Etransverse(r,φ) = cos(ωt - a) + cos(ωt - b) and I now know this describes an ellipse. So at any point, the Et vector goes in an ellipse. This suggests to me that if you had a Maple arrow graph animation, the arrows would move in a very complicated way. The "current" in the wire then looks different geometrically at each instant in time! So you would have to print out a sequence of 2D arrow graphs to get the nature of things. Idea. Go back to the complex form Et = ejmφe-jωt(Eφ + Er ) = ejmφ e-jωt(Eφ[-sinφ + cosφ ] + Er [cosφ + sinφ ] ) = ejmφ e-jωt( (Ercosφ - Eφsinφ) + (Er sinφ + Eφcosφ) ) Well never mind, there is no Er±jEφ sitting here.