6. Let's derive the doppler effect for EM waves. Suppose that in frame S there is an electromagnetic wave described by E(x, y, z) = Eo cos(kx – wt) ŷ, B(x, y, z) = (Eo/c) cos(kx – wt) 2, where k=w/c. Another frame 5 is moving along the - direction at speed v relative to frame S. Show that the wave appears in frame S as E(x, y, z) = Eo cos(kx – wt) ŷ, B(x, y, z) = (Eo/c) cos(kx – wt) 2, and find the relations between E and Eº, k and k, and w and @. In particular, is the wave red- shifted (@w)?
6. Let's derive the doppler effect for EM waves. Suppose that in frame S there is an electromagnetic wave described by E(x, y, z) = Eo cos(kx – wt) ŷ, B(x, y, z) = (Eo/c) cos(kx – wt) 2, where k=w/c. Another frame 5 is moving along the - direction at speed v relative to frame S. Show that the wave appears in frame S as E(x, y, z) = Eo cos(kx – wt) ŷ, B(x, y, z) = (Eo/c) cos(kx – wt) 2, and find the relations between E and Eº, k and k, and w and @. In particular, is the wave red- shifted (@w)?
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Transcribed Image Text:6.
Let's derive the doppler effect for EM waves. Suppose that in frame S there is an
electromagnetic wave described by
E(x, y, z) = Eo cos(kx – wt) ŷ,
B(x, y, z) = (Eo/c) cos(kx - wt) 2,
where k=w/c. Another frame 5 is moving along the - direction at speed v
relative to frame S. Show that the wave appears in frame S as
E(x, y, z) = Eo cos(kx – wt) ŷ,
B(x, y, z) = (Eo/c) cos(kx – wt) 2,
and find the relations between E, and E, k and k, and w and @. In particular, is the wave red-
shifted (w) or blue-shifted (@ >w)?
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