Consider the functions E, H : R³ × R → R³ given by: E(x, t) e cos(kx – wt) = H(x, t) = h cos(kx - wt) We want to show that under appropriate conditions on e, h, k = R³ and w€ R, these functions satisfy the Maxwell's equations in vacuum: €0 440 JE Ət SH Ət rot H = -rot E where μ = 1.2566 × 10-6 and 0 8.854 × 10-12 As are physical constants. - THE VEDNO = A-m = Additionally, we want to show that for æ(t) = t, the quantities E(x(t), t) and H(x(t), t) remain constant.
Consider the functions E, H : R³ × R → R³ given by: E(x, t) e cos(kx – wt) = H(x, t) = h cos(kx - wt) We want to show that under appropriate conditions on e, h, k = R³ and w€ R, these functions satisfy the Maxwell's equations in vacuum: €0 440 JE Ət SH Ət rot H = -rot E where μ = 1.2566 × 10-6 and 0 8.854 × 10-12 As are physical constants. - THE VEDNO = A-m = Additionally, we want to show that for æ(t) = t, the quantities E(x(t), t) and H(x(t), t) remain constant.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the functions E, H: R³ x R → R³ given by:
E(x, t) e cos(kx - wt)
=
H(x, t) = h cos(kx - wt)
-
We want to show that under appropriate conditions on e, h, k = R³ and w€ R, these
functions satisfy the Maxwell's equations in vacuum:
€0
μου
JE
Ət
OH
Ət
=
-
rot H
-rot E
where μ = 1.2566 × 10-6 V-s
and E0
A-m
V-m are physical constants.
k 1
||k|
Additionally, we want to show that for æ(t) = √t, the quantities E(x(t), t) and
H(x(t), t) remain constant.
8.854 x 10-12 A-s
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