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Final_sol

# Final_sol - Problem1 A radar system produces pulses...

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Unformatted text preview: Problem1. A radar system produces pulses consisting of 100 full cycles of a sinusoidal 70-GHz electromagnetic wave. The average power while the transmitter is on is 45 MW, and the waves are confined to a beam 20 cm in diameter. Find (a) the peak electric field, (b) the wavelength, (c) the total energy in pulse, and (d) a total momentum in a pulse. (e) If the transmitter produces 1000 pulses per second, what is the averaged power output? Solution: (a) The average intensity in a pulse is the average power during the pulse divided by the beam area S = P A (1 point) and the peak electric field is (2 points) E p = 2 μ cS ≈ 1.04 MV m . (b) (1 point) λ = c f = 4.29 × 10- 3 m . (c) (2 points) Duration of 100 full cycles is t = 100 f = 1.43 × 10- 9 s , so the total energy in a pulse is ∆ U = Pt = 6.43 × 10- 2 J . (d) (2 points) Using the formula ∆ p = ∆ U c we obtain ∆ p = 2.14 × 10- 10 kgm s . (e) (2 points) Since duration of one pulse is t = 1.43 × 10- 9 s , the duration of 1000 pulses will be t 1 = 10 3 × 1.43 × 10- 9 s = 1.43 × 10- 6 s . The averaged power output of the transmitter with 1000 pulses is P = Pt 1 1 s = 64.3 W Problem 2. Two homogeneous isotropic dielectrics have a boundary plane z = 0. For z > 0 the dielectric constant (relative permittivity) is K E 1 = 4 and for z < 0 K E 2 = 3 . A uniform electric field r E 1 = 5 ˆ i - 2 ˆ j + 3 ˆ k kV/m exists for z > 0. Find (a) r E 2 for z < 0...
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Final_sol - Problem1 A radar system produces pulses...

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