A microwave source produces pulses of 30.0-GHz radiation, with each pulse lastin

Question

A microwave source produces pulses of 30.0-GHz radiation, with each pulse lasting 1.00 ns. A parabolic reflector with a face area of radius 8.50 cm is used to focus the microwaves into a parallel beam of radiation, as shown in figure below. The average power during each pulse is 27.0 kw. (a) What is the wavelength of these microwaves? cm (b) What is the total energy contained in each pulse? mu J (c) Compute the average energy density inside each pulse. mJ/m^3 (d) Determine the amplitude of the electric field and magnetic field in these microwaves. E_max = kV/m B_max = mu T (e) Assuming that this pulsed beam strikes an absorbing surface, compute the force exerted on the surface during the 1.00-ns duration of each pulse. mu N

Explanation / Answer

f = 30 GHz, t = 1ns, r = 8.5 cm

P = 27 kW

(a) lamda = c/f

= 3*10^8/(30*10^9) = 0.01 m

lamda = 1 cm

(b) U = P*t

= 27*1000*1*10^-9 = 2.7*10^-5 J

U = 27 uJ

(c) u = U/V = U/(pir^2*ct)

u = 2.7*10^-5/(3.14*0.085^2*3*10^8*10^-9)

u = 0.00397 J/m^3

u = 3.97 mJ/m^3

(d) S = u.c = E^2/cuo

E = c(2uo*u)^0.5

E = (3*10^8)(2*4*3.14*10^-7*0.00397)^0.5

E = 3*10^5 V/m

E = 300 kV/m

B = E/c = 3*10^5/(3*10^8)

B = 10^-3 T

B = 1000 uT

(e) F = (Sav/c)*pi*r^2

F = (E^2/2c^2uo)(pi*r^2)

F = (3*10^5)^2*3.14*(0.085)^2/(2*9*10^16*4*3.14*10^-7)

F = 9.03*10^-3 N

F = 9030 uN

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