Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 31, Problem 62P
To determine
The proof that
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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?
Three electromagnetic waves travel through a certain point P along an x axis. They are polarized parallel to a y axis, with the following variations in their amplitudes. Find their resultant at P.
E1 = (5.0 × 10-5 V/m) sin[(4.0 × 1014 rad/s)t]
E2 = (7.0 × 10-6 V/m) sin[(4.0 × 1014 rad/s)t + 45˚]
E3 = (7.0 × 10-6 V/m) sin[(4.0 × 1014 rad/s)t - 45˚]
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.
Chapter 31 Solutions
Physics for Scientists and Engineers
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- 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.arrow_forwardThree electromagnetic waves travel through a certain point P along an x axis. They are polarized parallel to a y axis, with the following variations in their amplitudes. Find their resultant at P. E₁ (5.0 x 10-5 V/m) sin[(3.0 x 1014 rad/s)t] -E2= (6.0 x 10-6 V/m) sin((3.0 x 1014 rad/s)t + 45°] E3 = (6.0 x 10-6 V/m) sin[(3.0 x 1014 rad/s)t-45*] E = ( i i ✓) sin[(i x 1014 )t +arrow_forwardAn 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)arrow_forward
- The electric field and magnetic field in a sinusoidal electromagnetic wave which propagates in vacuum are given by E = (0.33î + bj)Emax Sin(kz – wt) B = (aî + 0.29 + yk)Bmax sin(kz + ôwt) where Emax = 2 V/m, k = 10° rad/m, w = 3 x 1014 rad/s and b, a, 7, 8 are some real numbers compatible with the properties of electromagnetic waves. Which of the following the value of y + baổ ? A) 0.9 B) -0.9 C) 1.81 D) -1.81 E) -0.45arrow_forwardThe electric field and magnetic field in a sinusoidal electromagnetic wave which propagates in vacuum are given by E- (0.51i + bị)Emaz sin(kz - wt) B (ai +0.59j + yk)Bmaxsin(kz + Swt) where Emax = 2 V/m, k = 10® rad/m, w 3 x 1014 rad/s and b, a, y, 8 are some real numbers compatible with the properties of electromagnetic waves. Which of the following is the value of y + bad? O 1.40 O -0.35 -0.70 O -1.40 O 0.70 O 0 0 0 0arrow_forwardWe 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 vectorarrow_forward
- The electric field and magnetic field in a sinusoidal electromagnetic wave which propagates in vacuum are given by E = (0.22i + bj)Emax Sin(kz- wt) B= (ai + 0.48ŷ +yk)Bmax sin(kz + dwt) %3D where Emax = 2 V/m, k = 10° rad/m, w = 3 x 104 rad/s and b, a, y, 8 are some real numbers compatible with the properties of electromagnetic waves. %3D Which of the following is the value of y + bað ? O 0.89 O - 0.89 O -0.45 O -1.79 O 1.79arrow_forwardA planar electromagnetic wave is traveling in the +x direction. At a certain point P and at given instant, the electric field of the wave is given by É = (0.09 V/m) f. (c = 3.0 x 108 /s, µ0 = 4x × 10-7 T·m/A, s0 = 8.85 × 10-12 C2/N · m²) What is the magnitude and direction of the B field (B)? O What is the Poynting vector at the point P at that instant? What is the energy density of the wave?arrow_forwardPlease 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)arrow_forward
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