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MIT 8 02T - Study Notes

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1 Concept Questions with Answers 8.01 W14D1 2 W14D1: Maxwell’s Equations and Electromagnetic Waves Today’s Reading Course Notes: Sections 13.5-13.7 3 Concept Question: Wave Number The graph shows a plot of the function The value of k is 1. k = 2π/ (2 m)2. k = 2π/ (1 m)3. k = 2π/ (0.5 m)4. k = 2π/ (4 m) y(x,0) = cos(kx)4 Concept Q. Answer: Wave Number Wavelength is 4 m so wave number is Answer: 4. k = 2π/ (4 m) k = 2π/λ= 2π/ (4 m)2 5 Concept Question: Direction of Propagation The figure shows the E (yellow) and B (blue) fields of a plane wave. This wave is propagating in the 1. +x direction 2. –x direction 3. +z direction 4. –z direction 6 Concept Question Answer: Propagation The propagation direction is given by the (Yellow x Blue) Answer: 4. The wave is moving in the –z direction dirE ×B7 Concept Question: Traveling Wave The B field of a plane EM wave is The electric field of this wave is given by B( y,t) = B0sin(ky −ωt)ˆk 1.E( y,t) = E0sin(ky −ωt)ˆj 2.E( y,t) = E0sin(ky −ωt)(−ˆj) 3.E( y,t) = E0sin(ky −ωt)ˆi 4.E( y,t) = E0sin(ky −ωt)(−ˆi)8 Concept Q. Ans.: Traveling Wave From the argument of the , we know the wave propagates in the positive y-direction. Answer: 4. E( y,t) = E0sin(ky −ωt)(−ˆi) So we have ˆE ׈B = ?׈k =ˆj ⇒ˆE = −ˆi sin(ky −ωt)3 Concept Question EM Wave 9 E(z,t ) = E0sin(kz +ωt)ˆjThe magnetic field of this wave is given by: The electric field of a plane wave is: 1.B(z,t) = B0sin(kz +ωt)ˆi 2.B(z,t) = B0sin(kz +ωt)(−ˆi) 3.B(z,t) = B0sin(kz +ωt)ˆk 4.B(z,t) = B0sin(kz +ωt)(−ˆk )10 Concept Q. Ans.: EM Wave From the argument of the , we know the wave propagates in the negative z-direction. Answer: 1. B(z,t) = B0sin(kz +ωt)ˆi So we haveˆE ׈B =ˆj × ? = −ˆk ⇒ˆB =ˆi sin(kz


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MIT 8 02T - Study Notes

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