Chapter 33, Problem 027 A plane electromagnetic wave, with wavelength 3.7 m, tra

Question

Chapter 33, Problem 027 A plane electromagnetic wave, with wavelength 3.7 m, travels in vacuum in the positive direction of an x axis. The electric field, of amplitude 430 V/m, oscillates parallel to the y axis. What are the (a) frequency, (b) angular frequency, and (c) angular wave number of the wave? (d) What is the amplitude of the magnetic field component? (e) Parallel to which axis does the magnetic field oscillate? (f) What is the time- averaged rate of energy flow associated with this wave? The wave uniformly illuminates a surface of area 2.7 m2. If the surface totally absorbs the wave, what are (g) the rate at which momentum is transferred to the surface and (h) the radiation pressure? (a) Number 8.11E7 (b) Number 5.09E8 (c)Number 1.70 (d) Number 1.43E-6 (e) z (f) Number (g) Number (h) Number Show Work is REQUIRED for this question: Hz Units Units rad/s Units rad/m or m-1 Units Units Units Units Open Show Work

Explanation / Answer

(A) f = c / lambda = (3 x 10^8)/3.7

= 8.11 x 10^7 Hz

(b) w = 2 pi f =5.09 x 10^8 rad/s

(C) k = 2 pi / lambda = 1.70 rad/m-1

(D) B = E / c = 1.43 x 10^-6 T

(E) along x axis.

(f) Intensity = E B / 2 u0 = 245.2 W/m^2

  
rate of energy flow = I A = (245.2)(2.7) = 662 W

(g) momentum transferred = (662 W) / (3 x 10^8)

= 2.21 x 10^-6 kg m/s^2

(h) P = rate of momentum transferred / Area

P = 8.17 x 10^-7 Pa

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