32. Electromagnetic Waves

A communications truck with a 44-cm-diameter dish receiver on the roof starts out 10 km from its base station. It drives directly away from the base station at 50 km/h for 1.0 h, keeping the receiver pointed at the base station. The base station antenna broadcasts continuously with 2.5 kW of power, radiated uniformly in all directions. How much electromagnetic energy does the truck's dish receive during that 1.0 h?

Consider current I passing through a resistor of radius r, length L, and resistance R. Show that the flux of the Poynting vector (i.e., the integral of $\overrightarrow{S}\cdot d\overrightarrow{A}$) over the surface of the resistor is I²R. Then give an interpretation of this result.

What is the intensity of an electromagnetic wave with a peak electric field strength of $125V/m$? (Assume the wave is in vacuum and use $c=3.00\times {10}^{8}m/s$ and $\epsilon 0_{}=8.85\times {10}^{-}C{2}^{/}$)

How large an emf (rms) will be generated in an antenna that consists of a circular coil 2.2 cm in diameter having 280 turns of wire, when an EM wave of frequency 810 kHz transporting energy at an average rate of 1.0 x 10⁻⁴ W/m² passes through it? [Hint: You can use Eq. 29–4 (for a generator) because that equation can be applied to an observer moving with the generator’s coil as it rotates at ω = 2𝝅f with f the frequency of the magnetic field.]

A point source light bulb emits uniformly in all directions with a total power output of $60W$. At a distance of $2.0m$ from the bulb, what is the light intensity?

At one instant, the electric and magnetic fields at one point of an electromagnetic wave are $E=(200\hat{i}+300\hat{j}-50\hat{k})\text{ V/m}$ and $B=B_0(7.3\hat{i}-7.3\hat{j}+a\hat{k}\mu T$. What is the Poynting vector at this time and position?

How practical is solar power for various devices? Assume that on a sunny day, sunlight has an intensity of 1000 W/m² at the surface of Earth and that a solar-cell panel can convert 20% of that sunlight into electric power. Calculate the area A of solar panel needed to power (c) a car that would require 120 hp. (d) In each case, would the area A be small enough to be mounted on the device itself, or in the case of (b) on the roof of a house?

When the Voyager 2 spacecraft passed Neptune in 1989, it was 4.5×10⁹ km from the earth. Its radio transmitter, with which it sent back data and s, broadcast with a mere 21 W of power. Assuming that the transmitter broadcast equally in all directions, What signal intensity was received on the earth?

How practical is solar power for various devices? Assume that on a sunny day, sunlight has an intensity of 1000 W/m² at the surface of Earth and that a solar-cell panel can convert 20% of that sunlight into electric power. Calculate the area A of solar panel needed to power (a) a calculator that consumes 50 mW (b) a hair dryer that consumes 1875 W.

If a microwave oven operates at a frequency of $2.4\times 109^{\mathrm{Hz}}$ and the intensity inside the oven is $2800 W/m^2$, what is the amplitude of the electric field of the microwaves inside the oven? (Assume the speed of light $c=3.0\times 108^m/s$ and vacuum permittivity $\epsilon =8.85\times 10{-12}^F/m$.)

Suppose you have a car with a 100-hp engine. How large a solar panel would you need to replace the engine with solar power? Assume that the solar panels can utilize 20% of the maximum solar energy that reaches the Earth’s surface (1000 W/m²). Explain why or why not this is practical.

We saw earlier (Chapter 19) that the rate energy reaches the Earth from the Sun (the “solar constant”) is about 1.3 x 10³ W/m². What is (a) the apparent brightness b of the Sun, and (b) the intrinsic luminosity L of the Sun?