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11 - EM Waves - Physics 8B 11 EM Waves rev 4.0 11 EM Waves...

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Physics 8B 11 – EM Waves rev 4.0 11 – EM Waves 1. Shown below are mathematical and pictorial representations of an electromagnetic plane wave propagating through empty space. The electric field is parallel to the z- axis; the magnetic field is parallel to the y-axis. Note: x ˆ , y ˆ , and z ˆ are unit vectors along the +x, +y, and +z directions, respectively. E(x, y, z, t) = E 0 sin(kx + ω t) z ˆ B(x, y, z, t) = B 0 sin(kx + ω t) y ˆ y 4 B 3 x 1 z E •2 a) Q: In which direction is the wave propagating? Explain. b) Q: Is the wave transverse or longitudinal? Explain. c) Q: Points 1, 2 and 3 lie in the x-z plane and point 4 lies in the x-y plane. For the instant shown, rank these points according to the magnitude of the electric field. d) Q: Is your ranking consistent with the mathematical expression for the electric field? Explain. e) Q: For the instant shown, rank points 1, 2, 3 and 4, according to the magnitude of the magnetic field. f) Q: Is your ranking consistent with the mathematical expression for the magnetic field? Explain.
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Physics 8B 11 – EM Waves rev 4.0 2. A simple periodic wave of electromagnetic radiation is moving in the direction shown below. P, Q, R, S and T are equally spaced points in the path of the wave. The distance PQ = d, the velocity of the wave is c, and its wavelength is 4d. An observer at T, looking towards P, would see H and D as vertically upwards, while E, A and B 1 would be horizontal and to their left. At a given instant, the magnetic field at P is a maximum, and is represented by the vector B 1 . D H P C Q R G B 1 S A T E Direction of B propagation F a) Q: Draw the electric field vector at point P at the same instant. Explain how you chose the direction.
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