16.5 The Electromagnetic Spectrum

How do the electromagnetic waves for the different kinds of electromagnetic radiation differ?

Accelerating electric charge emits electromagnetic radiation. How does this apply in each case: (a) radio waves, (b) infrared radiation.

Part of the light passing through the air is scattered in all directions by the molecules comprising the atmosphere. The wavelengths of visible light are larger than molecular sizes, and the scattering is strongest for wavelengths of light closest to sizes of molecules.
(a) Which of the main colors of light is scattered the most? (b) Explain why this would give the sky its familiar background colo…

Certain orientations of a broadcast television antenna give better reception than others for a particular station. Explain.

Is the visible region a major portion of the electromagnetic spectrum?

Radio waves normally have their E and B fields in specific directions, whereas visible light usually has its E and B fields in random and rapidly changing directions that are perpendicular to each other and to the propagation direction. Can you explain why?

Illustrate that the size of details of an object that can be detected with electromagnetic waves is related to their wavelength, by comparing details observable with two different types (for example, radar and visible light).

In what range of electromagnetic radiation are the electromagnetic waves emitted by power lines in a country that uses 50-Hz ac current?

A leaky microwave oven in a home can sometimes cause interference with the homeowner’s WiFi system. Why?

If you wish to detect details of the size of atoms (about 0.2 nm) with electromagnetic radiation, it must have a wavelength of about this size. (a) What is its frequency? (b) What type of electromagnetic radiation might this be?

(a) Calculate the wavelength range for AM radio given its frequency range is 540 to 1600 kHz. (b) Do the same for the FM frequency range of 88.0 to 108 MHz.

An outdoor WiFi unit for a picnic area has a 100-mW output and a range of about 30 m. What output power would reduce its range to 12 m for use with the same devices as before? Assume there are no obstacles in the way and that microwaves into the ground are simply absorbed.

A computer user finds that his wireless router transmits data at a rate of 75 Mbps (megabits per second). Compare the average time to transmit one bit of data with the time difference between the wifi signal reaching an observer’s cell phone directly and by bouncing back to the observer from a wall 8.00 m past the observer.

What are the wavelengths of (a) X-rays of frequency $2.0 \times 10^{17} \text{Hz}?$ (b) Yellow light of frequency $5.1 \times 10^{14} \text{Hz}?$ (c) Gamma rays of frequency $1.0 \times 10^{23} \text{Hz}?$

A radio transmitter broadcasts plane electromagnetic waves whose maximum electric field at a particular location is $1.55 \times 10^{−3} \text{V}/\text{m} .$ What is the maximum magnitude of the oscillating magnetic field at that location? How does it compare with Earth’s magnetic field?

During normal beating, the heart creates a maximum 4.00-mV potential across 0.300 m of a person’s chest, creating a 1.00-Hz electromagnetic wave. (a) What is the maximum electric field strength created? (b) What is the corresponding maximum magnetic field strength in the electromagnetic wave? (c) What is the wavelength of the electromagnetic wave?

A certain 60.0-Hz ac power line radiates an electromagnetic wave having a maximum electric field strength of 13.0 kV/m. (a) What is the wavelength of this very-low-frequency electromagnetic wave? (b) What type of electromagnetic radiation is this wave (b) What is its maximum magnetic field strength?

In a region of space, the electric field is pointed along the x-axis, but its magnitude changes as described by
$\begin{matrix}E_{x} = \left(10 \text{N}/\text{C}\right) \text{sin} \left(20 x - 500 t\right) \\ E_{y} = E_{z} = 0\end{matrix}$
where t is in nanoseconds and x is in cm. Find the displacement current through a circle of radius 3 cm in the $x = 0$ plane at $t = 0$.

Use the Appendix D for the next two exercises

Galileo proposed measuring the speed of light by uncovering a lantern and having an assistant a known distance away uncover his lantern when he saw the light from Galileo’s lantern, and timing the delay. How far away must the assistant be for the delay to equal the human reaction time of about 0.25 s?

Use the Appendix D for the next two exercises

On its highest power setting, a microwave oven increases the temperature of 0.400 kg of spaghetti by $45.0 ° \text{C}$ in 120 s. (a) What was the rate of energy absorption by the spaghetti, given that its specific heat is $3.76 \times 10^{3} \text{J}/\text{kg} \cdot ° \text{C}$ ? Assume the spaghetti is perfectly absorbing. (b) Find the average intensity of the microwaves, given that they are absorbed over a circular area…

Use the Appendix D for the next two exercises

Electromagnetic radiation from a 5.00-mW laser is concentrated on a $1.00 -\text{mm}^{2}$ area. (a) What is the intensity in $\text{W}/\text{m}^{2}$ ? (b) Suppose a 2.00-nC electric charge is in the beam. What is the maximum electric force it experiences? (c) If the electric charge moves at 400 m/s, what maximum magnetic force can it feel?

Use the Appendix D for the next two exercises

Suppose a source of electromagnetic waves radiates uniformly in all directions in empty space where there are no absorption or interference effects. (a) Show that the intensity is inversely proportional to $r^{2}$, the distance from the source squared. (b) Show that the magnitudes of the electric and magnetic fields are inversely proportional to r.

Use the Appendix D for the next two exercises

The Poynting vector describes a flow of energy whenever electric and magnetic fields are present. Consider a long cylindrical wire of radius r with a current I in the wire, with resistance R and voltage V. From the expressions for the electric field along the wire and the magnetic field around the wire, obtain the magnitude and direction of the Poyntin…

Use the Appendix D for the next two exercises

If a Lightsail spacecraft were sent on a Mars mission, by what ratio of the final force to the initial force would its propulsion be reduced when it reached Mars?

Use the Appendix D for the next two exercises

Radar is used to determine distances to various objects by measuring the round-trip time for an echo from the object. (a) How far away is the planet Venus if the echo time is 1000 s? (b) What is the echo time for a car 75.0 m from a highway police radar unit? (c) How accurately (in nanoseconds) must you be able to measure the echo time to an airplane 1…

Use the Appendix D for the next two exercises

How does the wavelength of radio waves for an AM radio station broadcasting at 1030 KHz compare with the wavelength of the lowest audible sound waves (of 20 Hz). The speed of sound in air at $20 °\text{C}$ is about 343 m/s.

A particle of cosmic dust has a density $\rho = 2.0 \left( \text{g}/\text{cm}\right)^{3} .$ (a) Assuming the dust particles are spherical and light absorbing, and are at the same distance as Earth from the Sun, determine the particle size for which radiation pressure from sunlight is equal to the Sun’s force of gravity on the dust particle. (b) Explain how the forces compare if the particle radius is smaller. (c) Explain what this implies about t…