Page 1 of 1
Problem 2: Spherical Waves The simplest possible spherical wave solution to Maxwell's equations is: (1/kr) sin u] = E(r,
Posted: Fri May 06, 2022 7:00 am
by answerhappygod
- Problem 2 Spherical Waves The Simplest Possible Spherical Wave Solution To Maxwell S Equations Is 1 Kr Sin U E R 1 (117.97 KiB) Viewed 57 times
Problem 2: Spherical Waves The simplest possible spherical wave solution to Maxwell's equations is: (1/kr) sin u] = E(r, 0, t) E(r, 0, 0, t) A sin [cos u - = r where u = kr wt and, as always, w = ck. Question 2.1: Show that the 3-D wave equation in vacuum is obeyed by this solution. The 3-D wave equation is: ²E V²E = 1 The vector Laplacian in spherical coordinates can be found here: c² Ət²
https://mathworld.wolfram.com/VectorLaplacian.html HINT: this problem is straight forward but has a lot of terms. Writing things in terms of u is helpful. Make sure you only keep non-zero terms and use the chain rule.