Maxwell's equations relating the electric field E and the magnetic field H as they vary with time in a vacuum are given as follows: divĒ = 0 (1) divĦ = 0 (2) curlĒ = (3) c ôt curlà (4) c ôt where c is the speed of light (pretty fast). (a) Using Maxwell's equations, show 1 ?Ē V × (V × Ē) (5) c2 Ət2 (b) Using Maxwell's equations, show (V . V)Ẽ = (6) c2 Ət2 You may find vector operator identity 3.38 from your textbook helpful: V x (V × F) = V(V · F) – v²F. (7)
Maxwell's equations relating the electric field E and the magnetic field H as they vary with time in a vacuum are given as follows: divĒ = 0 (1) divĦ = 0 (2) curlĒ = (3) c ôt curlà (4) c ôt where c is the speed of light (pretty fast). (a) Using Maxwell's equations, show 1 ?Ē V × (V × Ē) (5) c2 Ət2 (b) Using Maxwell's equations, show (V . V)Ẽ = (6) c2 Ət2 You may find vector operator identity 3.38 from your textbook helpful: V x (V × F) = V(V · F) – v²F. (7)
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Transcribed Image Text:2. Maxwell's equations relating the electric field E and the magnetic field H as they vary with
time in a vacuum are given as follows:
divE = 0
(1)
divÅ
(2)
curlE
(3)
c ôt
1 DE
curlH
(4)
с дё
where c is the speed of light (pretty fast).
(a) Using Maxwell's equations, show
V × (V × Ē)
(5)
c2 Ət2
(b) Using Maxwell's equations, show
(V . V)Ẻ =
(6)
c2 at2 *
You may find vector operator identity 3.38 from your textbook helpful:
V x (V × F) = V(V· F) – V²F.
(7)
Transcribed Image Text:V × (V × F) = V(V · F) – v²F.
(7)
(c) Use the results of the two parts above to show that
AẼ = 0.
(8)
c2 Ət?
(Such a relation between the time and space dependence of a function is called the wave
equation. You've probably seen it before, though maybe not in this specific form.)
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