Let ✰, ŷ be unit vectors in the positive x, y directions. A right-hand circular polarised wavetravelling in the positive z direction has an electric field vector given by---Er = Eo✰ cos(kz – wt) + Eoŷ cos(kz – wt − 2),and a corresponding left-hand circular polarised wave, with an additional phase shift of 6,has an electric field vector given byEL-=Eox cos(kz wt + 8) + Eoŷ cos(kz - wt ++ d).2Prove that the sum of these two circular polarised waves is equivalent to a single plane-polarised wave with its plane of polarisation at angle -8/2 from the x axis.

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Answered: Let ✰, ŷ be unit vectors in the…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter34: Maxwell’s Equations And Electromagnetic Waves

Section: Chapter Questions

Problem 77PQ

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What is the average magnitude of the Poynting vector 5.00 mi from a radio transmitter broadcasting isotropically (equally in all directions) with an average power of 250 kW?
A linearly polarized microwave of wavelength 1.50 cm is directed along the positive x axis. The electric field vector has a maximum value of 175 V/m and vibrates in the xy plane. Assuming the magnetic field component of the wave can be written in the form B = Bmax sin (kx t), give values for (a) Bmax, (b) k, and (c) . (d) Determine in which plane the magnetic field vector vibrates. (e) Calculate the average value of the Poynting vector for this wave. (f) If this wave were directed at normal incidence onto a perfectly reflecting sheet, what radiation pressure would it exert? (g) What acceleration would be imparted to a 500-g sheet (perfectly reflecting and at normal incidence) with dimensions of 1.00 m 0.750 m?
What is the physical significance of the Poynting vector?
The electric field of an electromagnetic wave is given by E=(6.0103V/m)sin[2(x18mt6.0 10 8s)] j Write the equations for the associated magnetic field and Poynting vector.
The magnetic field of a plane electromagnetic wave moving along the z axis is given by B =B0(coskz+t) j , where B0=5.001010 and k=3.10102m-1 . (a) Write an expression for the electric field associated with the wave. (b) What are the frequency and the wavelength of the wave? (C) What is its average Poynting vector?
Problem 2: a. An elliptically polarized plane wave traveling in the positive z-direction has electric field given by E = 10 sin (@t – Bz) ax + 15 sin (@t – Bz +45°) ay Find the poynting vector for this wave. b. Prove that a plane linearly polarized wave can be resolved into two circularly polarized wave traveling in the same direction but with opposite polarization orientations.
Let x and y components of the electric vector of an electromagnetic wave be given by Ex = a, sin ot and E₁ = a₂ sin(wt+6). Show that for 8 = 2nл where y n=1,2,3..., the electromagnetic wave is linearly polarized.
We have a plane wave in vacuum with direction of propagation along the wave vector K and angular frequency w. Eo is a complex but constant vector. Then, the electric field vector is E(r,t)=Re{E0 exp i (k.r-wt)} Deduce the following properties of a plane wave using Maxwell's equations and the material equations a) which condition has to be valid for the vectors k and E relatively to each other? b) calculate the magnetic field induction B in independence on the electric field vector C) calculate the Poynting vector in independence on the electric field vector
= The electric fields of two harmonic waves of angular frequency w, and we are given by E₁ E₁,0cos (k₁y + w₁t)i and E2 = E2,0cos (k₁y-w₂t)î. Find (a) the instantaneous Poynting vector for the resultant wave motion and (b) the time-average Poynting vector. If the direction of propagation of the second wave is reversed, find (c) the instantaneous Poynting vector for the resultant wave motion and (d) the time -average Poynting vector.
Consider a plane, monochromatic, electromagnetic wave traveling in a homogeneous medium, with index of refraction n = 1. Its magnetic field vector B in units of T is given by B₁ = 0 B₂ = 0 By = -9 × 10-8 sin(0.78x + 3.14 × 10³t)ŷ where t is seconds, and is in meters. a) Derive an expression for the electric field E associated with the magnetic field By. b) Find the direction of the the electric field from part a. c) Find the direction of the Poynting vector 5.
A plane wave is sent from space (y>0) with electrical parameters ɛ1=4ɛ0,µ1=µ0 to a medium (y 0,y0 to y<0.) b) Calculate the wavenumber in the first medium. c) Calculate the frequency of the wave. d) Calculate the wavenumber in the second medium.
The electric field of an electromagnetic wave travelling on a vacuum space is given by: Ex = 0, Ey = cos (2π × 10³ [t − Z]), E₂ = 0 where the amplitude is in V/m, t in second, x in meter and c= 300 000 000 m/s is the speed of light in vacuum. The vacuum permittivity is 8.85 × 10-¹² C²/m²N What is the wavelength (in meter)?. ....m. The average energy flux is n × 10-4 watt/m² What is the value of n? The amplitude of the magnetic field H is z × 10-4 A/m. What is the value of z?

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