3. The vector potential of a plane wave propagating in free space (vacuum) isgiven by A= 1.0 × 10¯15 (Tm) sin (10¹³t — kz)₁₁. (scalar potential is 0) (20)(a) What are the electric and magnetic fields of the wave? (10)(b) If this EM wave is coupled to square-shaped waveguide(0.0020mm X0.0020mm) by an focusing optics, how many modes are allowed to propagate? Whatare their propagating velocities? (group velocity) (10)

Part (a): Electric and Magnetic Fields from the Vector PotentialGiven the vector potential 𝐴⃗A for…

Answered: 3. The vector potential of a plane wave…

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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(11%) Problem 1: Consider an electromagnetic wave where the electric field of an electromagnetic wave is oscillating along the z-axis and the magnetic field is oscillating along the x-axis. 8 In what directions is it possible that the wave is traveling? (Select all that apply) OThe -z dırection. Grade Su OThe -y direction. OThe -x direction. OThe +z direction. V The +y direction. Deduction OThe +x direction. Potential Submissic Attempts
If the satellite antenna now transmits a 35kW signal, what is the maximum value of the electric field in 10 − 3 V/C?
Initial conditions are frequency 5 x10^6 Hz and current 1.5 A A magnetic far field of an antenna has the form B = (B_0sinθ/r) x (sin(kr − ωt)e_ϕ.) a) What is the phase of the wave at r = 6m when t = 0. b)Find the associated electric field and show a method to check this.
A radio station broadcasts its radio waves with a power of 50,000 W. What would be the intensity of this signal if it is received on a planet orbiting Proxima Centuri, the closest star to our Sun, at 4.243 ly away?
13. A certain 60.0 Hz AC power line radiates an electromagnetic wave having a maximum electric field strength of 27.5 kV/m. (a) What is the wavelength of this very low frequency electromagnetic wave? m(b) What is its maximum magnetic field strength? T
Hence show that the wave equation for the magnetic field is V²H+k²H=0 where k = ₁√√μ₁&
An industrial laser is used to burn a hole through a piece of metal. The average intensity of the light is 5 = 1.95 x 10⁹ W/m². What is the rms value of (a) the electric field and (b) the magnetic field in the electromagnetic wave emitted by the laser? (a) Number (b) Number i 2.23E6 i 4.06 Units nm + Units T +
Consider regions of the EM spectrum. In order to study the structure of a crystalline solid, you want to illuminate it with EM radiation whose wavelength is the same as the spacing of the atoms in the crystal (0.190 nm). A) What is the frequency of the EM radiation in Hertz? B) In what part of the EM spectrum (radio, visible, etc.) does it lie?
2. A sinusoidal electromagnetic wave with frequency 5.0x10“Hz travels in vacuum in the +x direction. The amplitude of electric field is 1.2x10³V/m. Find angular frequency w, wave number k, and amplitude of magnetic field. Write the wave function for the magnetic field in the form B = BmaxSin (wt –- kx).
6. The magnetic field intensity of an electromagnetic wave propagating in a lossless medium with e = 6€0 and µ = µo is given by Ĥ (y, t) = 24 sin(10't – ky + 7/6) (A/m) What is the corresponding k and Ē(y, t)?
A plane electromagnetic wave is traveling in a vacuum. The magnetic field is directed along the z-axis and given by: B, = 3.0µT sin ((1.0 × 107 )x - (3.0 × 1015 )t ) a) Determine the wavelength , of the wave. b) What is the frequency, f, of the wave in Hertz? c) Determine the maximum strength of the B-field. d) Determine the maximum strength of the E-field and it direction. e) Can you find a time and place when the B-field is zero? f) What is the strength of the E-field when the B-filed is zero?

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