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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
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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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
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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