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 byER=Eox cos(kz - wt) + Eoŷ cos(kz − wt-πT"and a corresponding left-hand circular polarised wave, with an additional phase shift of 8,has an electric field vector given byПEL=Eox cos(kz - wt + d) + 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.(You may quote suitable trigonometric identities from the Appendix).

The question asks you to prove that the sum of two circularly polarized waves is equivalent to a…

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?
The electric field of an electromagnetic wave traveling in vacuum is described by the following wave function: E =(5.00V/m)cos[kx(6.00109s1)t+0.40] j where k is the wavenumber in rad/m, x is in m, t s in Find the following quantities: (a) amplitude (b) frequency (c) wavelength (d) the direction of the travel of the wave (e) the associated magnetic field wave
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?
A device called an insolation meter is used to measure the intensity of sunlight. It has an area of 100 cm2 and registers 6.50 W. What is the intensity in W/m2?
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 electric part of an electromagnetic wave is given by E(x, t) = 0.75 sin (0.30x t) V/m in SI units. a. What are the amplitudes Emax and Bmax? b. What are the angular wave number and the wavelength? c. What is the propagation velocity? d. What are the angular frequency, frequency, and period?
The following represents an electromagnetic wave traveling in the direction of the positive y-axis: Ex=0;E0cos(kxt);Ez=0Bx=0;By=0;Bz=B0cos(kxt) The wave is passing through a wide tube of circular cross- section of radius R whose axis is along they-axis. Find the expression for the displacement current through the tube.
Figure P24.13 shows a plane electromagnetic sinusoidal wave propagating in the x direction. Suppose the wavelength is 50.0 m and the electric field vibrates in the xy plane with an amplitude of 22.0 V/m. Calculate (a) the frequency of the wave and (b) the magnetic field B when the electric field has its maximum value in the negative y direction. (c) Write an expression for B with the correct unit vector, with numerical values for Bmax, k, and , and with its magnitude in the form B=Bmaxcos(kxt) Figure P24.13 Problems 13 and 64.
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?
While outdoors on a sunny day, a student holds a large convex lens of radius 4.0 cm above a sheet of paper to produce a bright spot on the paper that Is 1.0 cm in radius, rather than a sharp focus. By what factor is the electric field in the bright spot of light related to the electric field of sunlight leaving the side of the lens facing the paper?
A parallel-plate capacitor has a plate area of A=0.250m2 and a separation of 0.0100 in. What must be must be the angular frequency w for a voltage V(t)=V0sint with V0=100V to produce a maximum displacement displacement current of 1.00 A between the plates?

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