A linearly polarized microwave of wavelength 1.49 cm is directed along the posit

Question

A linearly polarized microwave of wavelength 1.49 cm is directed along the positive x axis. The electric field vector has a maximum value of 180 V/m and vibrates in the xy plane. Assume that the magnetic field component of the wave can be written in the form

A linearly polarized microwave of wavelength 1.49 cm is directed along the positive x axis. The electric field vector has a maximum value of 180 V/m and vibrates in the xy plane. Assume that the magnetic field component of the wave can be written in the form B = Bmax sin (kx ? ?t). Find Bmax. Find k. Find ?. Calculate the average value of the Poynting vector for this wave. If this wave were directed at normal incidence onto a perfectly reflecting sheet, what radiation pressure would it exert? What acceleration would be imparted to a 455-g sheet (perfectly reflecting and at normal incidence) with dimensions of 1.00 m times 0.750 m?

Explanation / Answer

a. electric field and magnetic field are related by E = Bc

so B = E/c = 180/3*10^8

= 6*10-7 T   or 600 nT

Bmax = 600 nT

b. comparing this with general expression Bmax = Bsin (Kx-wt)

c. wave no. K = 2pi/L = 2*3.14 /0.0149 = 421.47 m^-1

as V = Lf

f = V/L = 3e8/0.0149 = 2*10^10 Hz

w= 2pif = 2*3.14* 2*10^10 =1.256 *10^11 rad/s

so expression for Bmax = 600nT sin ( 421.47x - 1.256*10^11 t)

d. poynting vector Sav = EB/uo = 600*10^-9 * 180/4pi*10^-7 = 86

Savg = 86/2 = 48 W/m^2

e. for a total refelctinf surface

Prad = 2I/c = 2* 48/3e8 = 3.2 *10^-7 Pa = 320 nPa

f. accleration = F/m = PA/m = 320*10^-9 * 0.75 *1/(0.455)

a = 5.274 *10^-7

a = 527.47 nm/s^2

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