# Linearly polarized microwave

A linearly polarized microwave of wavelength 1.49 cm is directed along the positive x axis. The electric field vector has a maximum value of180 V/m and vibrates in the $x y$ plane. Assume that the magnetic field component of the wave can be written in the form

$B = B_{max} sin (k_x ? ?t)$.

(a) Find $B_{max}$.

(b) Find k.

(c) Find ?.

(e) Calculate the average value of the Poynting vector for this wave. av

(f) If this wave were directed at normal incidence onto a perfectly reflecting sheet, what radiation pressure would it exert? $P_{rad}$

(g) What acceleration would be imparted to a 455–g sheet (perfectly reflecting and at normal incidence) with dimensions of 1.00 m × 0.750 m?

$Em/Bm = c$

$Bm = Em/c =180/3*10^8 =60*10^{-8}$ T

$k=2*pi/lambda = 2*pi/0.0149 =421.69 m^-{1}$

$lambda = C*T = C/F$

$F = C/lambda = 3*10^8/0.0149 =2.0134*10^10 s^-{1}$

$H = B/mu$

$S = 1/2*(E x H)=1/2(Em*B/mu) =0.5*(180*60*10^{-8}/4*pi*10^{-7}) =5.4*10^-5/4*pi*10^{-7} =$

$= 42.971 W/m^2$

$P = S/c =42.971/3*10^8 =1.432*10^{-7} N/m^2 =143.239 nPa$

$A =0.75 m^2$

$F = P*A =1.074*10^{-7} N$

$a =F/m =2.361*10^{-7} m/s/s =236.109 nm/s^2$