1.) A laser that emits pulses of UV lasting 3.25 ns has a beam diameter of 2.55
ID: 1283604 • Letter: 1
Question
1.)
A laser that emits pulses of UV lasting 3.25 ns has a beam diameter of 2.55 mm. If each burst contains an energy of 2.20 J, what is the length in space of each pulse? (in m)
What is the average energy per unit volume (the energy density) in one of these pulses?
(in J/m^3)
2.)
A 1.55 m long FM antenna is oriented parallel to the electric field of an EM wave. How large must the electric field be to produce a 1.39 mV (rms) voltage between the ends of the antenna?
(in V/m)
What is the rate of energy transport per square meter?
(in W/m^2)
3.
An AM radio transmitter broadcasts 58.0 kW of power uniformly in all directions. Assuming all of the radio waves that strike the ground are completely absorbed, and that there is no absorption by the atmosphere or other objects, what is the intensity 27.0 km away? (Hint: Half the power will be spread over the area of a hemisphere.)
(in W/m^2)
What is the maximum electric field strength at this distance?
(in mV/m)
Explanation / Answer
d = v t
d = 3 * 108 m/s * 3.25 * 10-9 s
d = 0.975 m
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Erms = Vrms / d
= 1.39 * 10-3 / 1.55
= 8.968 * 10-4 V/m
S = c epsilon E2rms = c epsilon V2rms/d
= 3 * 108 * 8.85 * 10-12 * (8.968 * 10-4)2
= 2.14 * 10-9 W/m2
---------------------------------------------
I = power / area
= 58000 / (4 pi * 270002)
I = 6.33 *10-6 W/m2
E2max = 6.33 *10-6 * 2 * 4pi * 10-7 * 3 * 108
Emax= 0.0691 V/m
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