A microwave source produces pulses of 20.0 GHz radiation, with each pulse lastin

Question

A microwave source produces pulses of 20.0 GHz radiation, with each pulse lasting 1.00 ns. A parabolic reflector (R = 6.00 cm) is used to focus these pulses into a parallel beam of radiation, as shown in the Figure. The average power during each pulse is 25.0 kW. a. What is the wavelength of these microwaves? b. What is the total energy contained in each pulse? c. Compute the average energy density inside each pulse. d. Determine the amplitude of the electric and magnetic fields in these microwaves. e. Compute the force exerted on the surface during the 1.00 ns duration of each pulse if the pulsed beam strikes on the absorbing surface.

Explanation / Answer

Given f = 20.0 GHz = 20x10^9 Hz

(a) Wavelength (lemda) = c / f = (3x10^8) / (20x10^9) = 0.15 x 10^-1 m = 1.5 cm

(b) t = 1.0 ns = 1x10^-9 s.

Total energy in each pulse, U = P x t = 25x10^3 x 1x10^-9 kW = 25x10^-6 J = 25 micro Joule.

(c) Average energy density inside each pulse -

Uav = U / volume = (25x10^-6) / (pi*r^2*l) = (25x10^-6) / (3.14*r^2*l) = (25x10^-6) / (3.14*r^2*c*delta t)

= (25x10^-6) / (3.14*0.06^2*3x10^8*10^-9) = 7.37x10^-3 J/m^3

(d) Write the expression -

Uav = (1/2)*epcelon0*Emax^2

=> Emax = sqrt[(2*Uav) / epcelon0] = sqrt[(2*7.37x10^-3 / (8.85x10^-12)]

= 4.08 x 10^4 V/m = 40.8 kV/m

Magnetic field, Bmax = Emax / c = (4.08 x 10^4) / (3.0x10^8) = 1.36 x 10^-4 T = 136 x 10^-6 T = 136 micro T

(e) Force, F = Uav*A = 7.37x10^-3xpi*r^2 = 7.37x10^-3x3.14x0.06^2 = 8.33 x 10^-5 N = 83.3 micro N.

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