32. Electromagnetic Waves

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 $\epsilon 0_{}=8.85\times {10}^{-}C{2}^{/}$)

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 $\epsilon =8.85\times 10{-12}^F/m$.)

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?

A 100 W lightbulb actually emits around only 10 W of light. What is the intensity of the light 1 cm away if the light is emitted perfectly spherically? What is the magnitude of the electric field emitted by the lightbulb? What about the magnetic field?

Suppose a 25-kW radio station emits EM waves uniformly in all directions. What is the rms voltage induced in a 1.0-m-long vertical car antenna (c) 1.0 km away, (d) 50 km away?

A radio receiver can detect signals with electric field amplitudes as small as 300 μV/m. What is the intensity of the smallest detectable signal?