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.

Answered: Image /qna-images/answer/83d7b9a2-8ea6-491f-9bfe-dcdc24d19912.jpg

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

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Assume the mostly infrared radiation from a heat lamp is IR-B and acts like a continuous wave with wavelength 2.90 μm. (a) If the lamp's 220 W output is focused on a person's shoulder, over a circular area 24.0 cm in diameter, calculate the intensity in (W/m²). W/m² (b) The shoulder area has a mass of 3.75 kg. Assume no other heat transfer and given its specific heat is 3.47 × 10³ J/(kg •°C), calculate the change in temperature if the shoulder is radiated for a time of 45.0 s. °C
Magnetic field intensity of a propagating wave in free space is given by H =0.3 cos(4*108t+ 2y) ax V/m the plot of H versus y at time, t = T/8
The following considers electromagnetic wave propagating in free-space (without charges or currents). (a) State the Maxwell's equations in terms of E and H for the free-space. (b) Should that the four equations are satisfied by: E = Eo cos (w²-t)) x Eo H = COS CHO for some constants Eo and co, where c is the speed of light in free-space. s(w (²-t))ỹ
The electric field Ē is given by Ē(y, t) = -(2.20 × 10° V/m)ksin[ky – (14.25 x 10²rad/s)t]. (i) What is the wavelength of the wave? (ii) What is the amplitude of the magnetic field of this wave? (iii) Write the vector equation for electric field? O a. (i) A = 13.09 × 10 °m (ii) 0.73 × 10 -³ T (iii) B = –(0.73 × 10 ³T)jsin[(4.75 × 10ʻrad/m)y – (14.25 × 10" rad/s)t] O b. (i) A = 13.09 × 10 5m (ii) 0.73 × 10 3 T (ii) B = –(0.73 × 10 ³T)isin[(4.75 × 10ʻrad/m)y + (14.25 x 10" rad/s)t] O c. (i) A = 13.09 × 10-5m (ii) 0.73 ×x 10 ³ T (iii) B = –(0.73 × 10 ³T)isin[(4.75 × 10ʻrad/m)y + (14.25 × 10²rad/s)t] С. O d. (i) A = 13.09 × 10-5m (ii) 0.73 × 10 -3 T (iii) B = –(0.73 × 10 ³T)êsin[(4.75 × 10ʻrad/m)y – (14.25 × 1012 rad/s)t] Ое.(i) А — 13.09 х 10 5т (i) 0.73 x 10 3 T (i) В: -(0.73 × 10-³T)åsin[(4.75 × 10ªrad/m)y - (14.25 x 102 rad/s)t]
Write the expression for the electric field E of a 300 MHz LH circularly polarized plane wave propagating in the -ve X-direction in a medium with ɛp. = 3, µ = 1, and σ = 5 (S/m).
Using Maxwells equations: V-E = O SH VO VE = -m dt JF Find 17 (xY₁Z₁+) = 110 cos(B, x+B₂y + B₂ Z-w+) and Assume that Elx, y, 2₁ +) = Eo cos (B₁ x + B₂y + B₁ Z=w+) Show that I and I are perpendicular and each is transverse to the direction of propagation V x H = ‹ JE ६
RF Electromagnetics: . If an x-component of the E-field varies as a sine function, and y-field component varies as a cosine function; assuming that the Ex=0.7Ey, what is the polarization of the resultant wave whichpropagates in the positive z-direction. For frequency f, write the full expression for the electricfield of a plane wave propagating in vacuum.
A plane wave is sent from space (y>0) with electrical parameters ɛ1=4ɛ0,µ1=µ0 to a medium (y <0) with electrical parameters ɛ2= 9ɛ0,u2=µ0 with an angle of Oi relative to the surface normal. The incoming electric field is given as: É;(x, y) = (e + Aẻ, + 3ẻ,)ei4nv3xej4Ty a) Find the angle of incidence (Oi) of the electromagnetic wave. b) Find the angles of reflection and refraction (transmission). c) What should be the value of the coefficient A for the wave to be plane? d) Calculate the magnetic field for the incoming electromagnetic wave.
. The electric field associated with an electromagnetic wave in vacuum is given by E = i 40 cos (kz - 6 x 10°t), where E, z and t are in V/m, metre and second, respectively. The value of wave vector k is (a) 2 m-1 (c) 6 m-1 (b) 0.5 m- (d) 3 m-1
A certain guided wave travels through air with the following magnetic field H=10+ y cos(157x) sin[(67×10° rad/s)t - Bz] [A/m] (0.3) Find the associated and B. There are a couple ways to solve this problem. Note: this is NOT a plane wave, and be sure to understand why. Nevertheless it IS a valid solution of Maxwell's equations. You will see how guided waves like this come about
= 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.
An example of a simple model based on atmospheric fluid dynamics is the Lorenz equations developed by the American meteorologist Edward Lorenz, 2. dx = -ox + oy dt (28.6) dy = rx - y - xZ dt (28.7) dz -bz + xy (28.8) dt Lorenz developed these equations to relate the intensity of atmospheric fluid motion, x, to temperature variations y and z in the horizontal and vertical directions, respectively. As with the predator-prey model, we see that the nonlinearity is localized in simple multiplicative terms (xz and xy). Use numerical methods to obtain solutions for these equations. Plot the results to visualize how the dependent variables change temporally. In addition, plot the dependent variables versus each other to see whether any interesting patterns emerge.

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