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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Similar questions

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
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
A regular sinusoidal plane wave, for which the following expression is given for the electric field intensity Ei(x,z)=ay10e-j(6z+8z) (V/m) The perfect conductor at z=0 hits the plane. a) Find the frequency and wavelength of the wave. b) Write the instantaneous expressions Ei(x,z;t) and Hi(x,z;t). c) Determine the angle of incidence. d)Find Er(x,z) and Hr(x,z) for the reflected wave.
A uniform plane wave, with electric field magnitude of 3 (mV/m), is propagating in a medium with µ, = 4. We know that this plane wave travels at a speed of co/8 where co is the speed of light in vacuum. The frequency of this wave is 1 GHz. The propagation direction is y direction. We also know that this plane wave is an LHCP wave. Find: a) The wavelength of the plane wave in this medium. b) The phasor form of the E field which exhibits all the characteristics given in the problem. c) The magnetic field H in the time domain.
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?
An electromagnetic plane wave is propagating with an intensity I =1.0×10° Wm² in a medium with = 3 e, and µ= Ho. The amplitude of the electric field inside the medium is x10' Vm (up to one decimal place). (e,= 8.85x10-12C?N¯'m², µ, = 47x10 NA,c= 3x10° ms)
The instantaneous expression of the electric field of a plane wave in air is given as Ei → = ý10cos (wt − x − 3 – √3 z) V / m. The wave reaches the perfectly conducting plane limit at z = 0. a) So what is the phase constant (k1) in air? b) What is the angle of incidence?
A plane wave is sent from space (y>0) with electrical parameters ɛ1=4ɛ0,u1=µ0 to a medium (y 0)?
Please solve ASAP Problem 1: The electric field in a radio (electromagnetic) plane wave is given by the equation(picture attached) E(x, t) = j0.09 sin(2.1r – 27 × 10^6 t) V/m with a in meters and t in seconds. All parts of this problem refer to this expression. a) What is the direction of propagation of this wave? Choose one: +x -x -y +y +z -z b) What is the polarization? Choose one: X y or z c) What is the wavelength? (Give a number, in meters) d) What is the frequency? (Give a number, in Hz) a) What is the direction of propagation of this wave? Choose one: +x -x -y +y +z -z b) What is the polarization? Choose one: X y or z c) What is the wavelength? (Give a number, in meters) d) What is the frequency? (Give a number, in Hz)
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.
= 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.

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