Question

. 1. The relations for the potential, electric and magnetic fields, and time averaged intensity are written in terms of spherical coordinates (cos θ pow ___ (_) sin[w(t-r/c)] V(r, θ, t) Scalar Potential: Hopow ATT -pop Α(r, θ,t) -sin[w(t-r/c)]2 Vector Potential: μοΡου-(-) cos[w(t-r/c)ja Electric Field: Ε--7V (3) 4π 7" Magnetic Field: B Vx A- 〈S) = (ww) sn-2- Intensity: Express these relationships in "coordinate-free" form, in which one is not committed to the spherical coordinate system. As an example, Po cose in Equation 1 may expressed in this manner by taking advantage of the fact that Pocos θ-Po

Answer 1

Solution iven hat →The relations to .lhe poten-lial electric and magnetic ieldsOre ime averagc intensi ines are rHten o1 spherical co-ordinate Scalar potentia Pocose Scalar potential in-Herms ol spherica Co-ordina ree- Beca us є 04 eo e knouo that d'pole terms tcrms ol POla co ordinale 7 Nouo Scalar polcntial fn Jree sphericat co-ordina l Sin wt

other ua Nector potential 411Ir in terms ot ree spherica cdin a te 11T t is some because here γ00 dependance or electnic Jield 4 TI rom eq ータ o stne Po coset

netic fe ld be come or rnsi-l, 6 3211 C As knouo that

lo uo 32 T1YC