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
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?
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?
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)
a) ($\mathbf{0.1}$ pts) Show that, given a vector field $\bar{V}$, V× (VV)=V(V · V) + V²Ñ b) ($\mathbf{0.2}$ pts) Starting from Maxwell's equations, demonstrate that the electric field $\bar{E}$ in three dimensions satisfies the vector wave equation V²Ē = 18²Ē c² at²
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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.
Assume that a light emitting diode (LED) emits a power P uniformly distributed over its forward hemisphere and zero power in its rear hemisphere. Model the light waves from the LED as being sinusoidal. (a) What is the amplitude of the wave’s electric field at a distance R? (b) Calculate the numerical value of the electric field amplitude if P = 10 W and R = 3.0 m.
Imagine a wave whose electric field is given by E= -E0cos(ky - wt) (k-direction), the corresponding B field points in what direction ? Please explain.
The intensity of a cylindrical laser beam is 0.800 W / m2 . Cross sectional area beam is 3.0 × 10−4 m2 , and the intensity is uniform throughout the cross section of the lightning. a) What is the average output power of the laser? b) What is the rms (rms) value of the electric field in the beam?
A number N of plane waves are travelling parallel; the waves share a common wavevector k and common direction of electric field vector along unit vector û, but each wave has its own distinct amplitude Eoi and phase difference 8. Therefore the ith wave (for 1 ≤ i ≤N) has electric field given by Ei = Eoiû Re [exp j(kr - wt + 8;)]. From this, prove that the total intensity Inet including interference is given by Inet = |Ec|2 270 where the complex amplitude Ę is defined by N Ec = Eoi exp(jdi), and no is the impedance of free space. i=1

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