A linearly polarized microwave of wavelength 1.5 cm is directed along the positi

Question

A linearly polarized microwave of wavelength 1.5 cm is directed along the positive x axis. The electric flied vector has a maximum value of 175 V/m and vibrates in the xy plane. (a) Assume that the magnetic field comp0onent of the wave can be written in the form B = B0 sin(kt - omegat) and give values for B0, k, and omega. Also determine in which plane the magnetic field vector vibrates. (b) Calculate the magnitude of the poynting vector for this wave. (c) What radiation pressure would this vae exert if directed at normal incidence onto a perfectly reflecting sheet? (d) What acceleration would be imparted to a 500-g sheet (perfectly reflecting and at normal incidence) with dimensions 1 m x 0.75 m?

Explanation / Answer

a) B = E0 / c = 175 / 3 x 108

= 5.833 * 10-7 T

= 583 nT

K = 2 * pi / Lambda = 2 * pi / (1.5 * 10-2)

= 419 = 4.19 x 102

w=K * c = 4.19 x 102 * 3 x 108

= 1.26 x 1011 rad/s

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b) S(avg) = 1/2 * (E B)2

= 1/2 * (175 * 583 x 10-9)2

= 5.20 x 10-9 J

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c) P = 2 E / c = 2 * 175 / (3 x 108)

= 1.167 x 10-6 = 1167 nPa

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d) Area A = 1 x 0.75 = 0.75 m2

a = PA / m = 1.167 x 10-6 x 0.75 / 500 x 10-3

= 1.750 * 10-6 = 1750 nm/s2

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