32. Electromagnetic Waves

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?

What is the total energy density in an electromagnetic wave of intensity 1000 W/m²?

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?

Consider current I passing through a resistor of radius r, length L, and resistance R. Determine the strength and direction of the Poynting vector at the surface of the resistor.

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.

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?

A microwave beam with a wavelength of 1.5 cm has an intensity of 25 W/m². What is the magnetic field amplitude?

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

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.

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?

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?