Solved: Estimate the rms electric field in the sunlight

Problem 1P (II) At a given instant, a 3.8-A current flows in the wires connected to a parallel-plate capacitor. What is the rate at which the electric field is changing between the plates if the square plates are 1.60 cm on a side?

The electric field in an EM wave traveling north oscillates in an east-west plane. Describe the direction of the magnetic field vector in this wave. Explain.

Problem 2P (Ill) A 1500-nF capacitor with circular parallel plates 2.0 cm in diameter is accumulating charge at the rate of 32.0 mC/s at some instant in time. What will be the induced magnetic field strength 10.0 cm radially outward from the center of the plates? What will be the value of the field strength after the capacitor is fully charged?

Problem 2Q Is sound an EM wave? If not, what kind of wave is it?

Problem 3Q Can EM waves travel through a perfect vacuum? Can sound waves?

Problem 4Q When you flip a light switch on. does the light go on immediately? Explain.

Are the wavelengths of radio and television signals longer or shorter than those detectable by the human eye?

Problem 6Q When you connect two loudspeakers to the output of a stereo amplifier, should you be sure the lead-in wires are equal in length to avoid a time lag between speakers? Explain.

In the electromagnetic spectrum, what type of EM wave would have a wavelength of \(10^3 \mathrm{~km}\) ? \(1 \mathrm{~km}\)? \(1 \mathrm{~m}\) ? \(1 \mathrm{~cm}\) ? \(1 \mathrm{~mm} ? 1 \mu \mathrm{m}\) ?

Problem 8Q Can radio waves have the same frequencies as sound waves (20 Hz-20,000 Hz)?

Problem 9P (I) How long does it take light to reach us from the Sun, 1.50 X 108 km away?

Problem 9Q If a radio transmitter has a vertical antenna, should a receiver's antenna (rod type) be vertical or horizontal to obtain best reception?

Problem 10P (I) A widely used "short-wave" radio broadcast band is referred to as the 49-m band. What is the frequency of a 49-m radio signal?

If a radio transmitter has a vertical antenna, should a receiver's antenna (rod type) be vertical or horizontal to obtain best reception?

Problem 11P (II) Our nearest star (other than the Sun) is 4.2 light-years away. That is, it takes 4.2 years for the light it emits to reach Earth. How far away is it in meters?

Problem 11Q Discuss how cordless telephones make use of EM waves. What about cell phones?

(II) A light-year is a measure of distance (not time). How many meters does light travel in a year?

Problem 12Q A lost person may signal by switching a flashlight on and off using Morse code. This is actually a modulated EM wave. Is it AM or FM? What is the frequency of the carrier, approximately?

Problem 13P (II) How long would it take a message sent as radio waves from Earth to reach Mars when Mars is (a) nearest Earth. (b) farthest from Earth? Assume that Mars and Earth are in the same plane and that their orbits around the Sun are circles (Mars is * 230 X 106 km from the Sun).

(II) What is the minimum angular speed at which Michelson's eight-sided mirror would have had to rotate to reflect light into an observer's eye by succeeding mirror faces (Fig. 22-10)?

(II) A student wants to scale down Michelson's lightspeed experiment to a size that will fit in one room. A six-sided mirror is available, and the stationary mirror can be mounted from the rotating mirror. If the arrangement is otherwise as shown in Fig. , at what minimum rate must the mirror rotate?

Problem 27P (I) What is the range of wavelengths for (a) FM radio (88MHzto 108 MHz) and (b) AM radio (535 KHz to 1700 KHz)?

Problem 28P (I) Estimate the wavelength for a 1 9-GHz cell phone transmitter.

Problem 36P (Ill) A 1.60-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 1.00-mV (rms) voltage between the ends of the antenna? What is the rate of energy transport per m2?

Problem 37GP If the Sun were to disappear or radically change its output, how long would it take for us on Earth to learn about it?

Problem 38GP Light is emitted from an ordinary lightbulb filament in wavetrain bursts about 10-8 in duration. What is the length in space of such wave trains?

Problem 41GP Problem Cosmic microwave background radiation fills space with an average energy density of about 4 x 10-14 J/m3. (a) Find the rms value of the electric field associated with this radiation, (b) How far from a 7.5-kW radio transmitter emitting uniformly in all directions would you find a comparable value?

Problem 50GP A radio station is allowed to broadcast at an average power not to exceed 25 kW. If an electric field amplitude of 0.020 V/m is considered to be acceptable for receiving the radio transmission, estimate how many kilometers away you might be able to detect this station.

Problem 43GP Estimate the rms electric field in the sunlight that hits Mars. Knowing that the Earth receives about 1350 W/m2 and that Mars is 1.52 times farther from the Sun (on average) than is the Earth.

A point source emits light energy uniformly in all directions at an average rate \(P_0\) with a single frequency . Show that the peak electric field in the wave is given by \(E_{0}=\sqrt{\frac{\mu_{0} c P_{0}}{2 \pi r^{2}}}\) Equation Transcription: Text Transcription: P_0 E_0=sqrt{mu_0cP_0 over 2pir^2}

Problem 3P If the magnetic field in a traveling EM wave has a peak magnitude of 17.5 nT at a given point, what is the peak magnitude of the electric field?

In an EM wave traveling west, the B field oscillates vertically and has a frequency of 80.0 kHz and an rms strength of \(6.75 \times 10^{-9} \mathrm T\). What are the frequency and rms strength of the electric field, and what is its direction? [Hint: see Fig. 22-7.]

Problem 5P What is the frequency of a microwave whose wavelength is 1.60 cm?

What is the wavelength of a \(29.75 \times 10^9-\mathrm{Hz}\) radar signal?

An EM wave has frequency \(9.66 \times 10^{14} \mathrm{~Hz}\). What is its wavelength, and how would we classify it?

Problem 8P An EM wave has a wavelength of 650 nm. What is its frequency, and how would we classify it?

A lost person may signal by flashing a flashlight on and off using Morse code. This is actually a modulated EM wave. Is it AM or FM? What is the frequency of the carrier, approximately?

(II) Who will hear the voice of a singer first-a person in the balcony away from the stage (Fig. ), or a person away at home whose ear is next to the radio? How much sooner? Assume that the microphone is a few centimeters from the singer and the temperature is \(20^{\circ} \mathrm{C}\). FIGURE 22-19 Problem 16 Equation Transcription: Text Transcription: 20^oC

(II) Pulsed lasers used in science and medicine produce very short bursts of electromagnetic energy. If the laser light wavelength is 1062 nm (this corresponds to a Neodymium-YAG laser), and the pulse lasts for 32 picoseconds, how many wavelengths are found within the laser pulse? How short would the pulse need to be to fit only one wavelength?

(I) The \(\mathrm {\vec{E}}\) field in an EM wave in free space has a peak of \(21.8 \mathrm{~mV} / \mathrm{m}\). What is the average rate at which this wave carries energy across unit area per unit time? Equation Transcription: Text Transcription: vector{E} 21.8 mV/m

Problem 19P The magnetic field in a traveling EM wave has an rms strength of 28.5 nT. How long does it take to deliver 235 J of energy to 1.00 cm2 of a wall that it hits perpendicularly?

Problem 20P How much energy is transported across a 1.00-cm2 area per hour by an EM wave whose E field has an rms strength of 38.6 mV/m?

(II) A spherically spreading EM wave comes from a 1200-W source. At a distance of 10.0 m, what is the average intensity, and what is the rms value of the electric field?

Problem 22P A 12.8-mW laser puts out a narrow beam 1.75 mm in diameter. What are the average (rms) values of E and B in the beam?

Problem 23P Estimate the average power output of the Sun, given that about 1350 W/m2 reaches the upper atmosphere of the Earth.

Problem 25P A high-energy pulsed laser emits a 1.0-ns-long pulse of average power 2.8 × 1011 W. The beam is 2.2 × 10?3 min radius. Determine (a) the energy delivered in each pulse, and (b) the rms value of the electric field.

Problem 24P If the amplitude of the B field of an EM wave is 2.5 × 10?7 T, (a) what is the amplitude of the Efield? (b) What is the average power per unit area of the EM wave?

Problem 26P Estimate the radiation pressure due to a 100-W bulb at a distance of 8.0 cm from the center of the bulb. Estimate the force exerted on your fingertip if you place it at this point.

Problem 29P Compare 940 on the AM dial to 94 on the FM dial. Which has the longer wavelength, and by what factor is it larger?

What are the wavelengths for two TV channels that broadcast at 54.0 MHz (Channel 2) and 806 MHz (Channel 69)?

Problem 31P The variable capacitor in the tuner of an AM radio has a capacitance of 2800 pF when the radio is tuned to a station at 550 kHz. What must the capacitance be for a station near the other end of the dial, 1610 kHz?

Problem 32P The oscillator of a 96.1-MHz FM station has an inductance of 1.8 µH. What value must the capacitance be?

Problem 33P A certain FM radio tuning circuit has a fixed capacitor C = 840 pF. Tuning is done by a variable inductance. What range of values must the inductance have to tune stations from 88 MHz to 108 MHz?

(II) An amateur radio operator wishes to build a receiver that can tune a range from \(14.0 \mathrm{MHz}\) to \(15.0 \mathrm{MHz}\). A variable capacitor has a minimum capacitance of \(82 \mathrm{pF}\). (a) What is the required value of the inductance? (b) What is the maximum capacitance used on the variable capacitor?

A satellite beams microwave radiation with a power of \(10 \mathrm{~kW}\) toward the Earth's surface, \(550 \mathrm{~km}\) away. When the beam strikes Earth, its circular diameter is about \(1500 \mathrm{~m}\). Find the rms electric field strength of the beam.

Problem 39GP (a) How long did it take for a message sent from Earth to reach the first astronauts on the Moon? (b) How long will it take for a message from Earth to reach the first astronauts who arrive on Mars; assume Mars is at its closest approach to Earth (78 × 106 km)?

A radio voice signal from the Apollo crew on the Moon (Fig. 22-20 ) was beamed to a listening crowd from a radio speaker. If you were standing 25 m from the loudspeaker, what was the total time lag between when you heard the sound and when the sound left the Moon?

Problem 42GP What are E0 and B0 2.00 m from a 95-W light source? Assume the bulb emits radiation of a single frequency uniformly in all directions.

Problem 44GP At a given instant in time, a traveling EM wave is noted to have its maximum magnetic field pointing west and its maximum electric field pointing south. In which direction is the wave traveling? If the rate of energy flow is 560 W/m2, what are the maximum values for the two fields?

Estimate how long an AM antenna would have to be if it were \((a)\ \frac{1}{2} \lambda\) or \((b)\ \frac{1}{4} \lambda\). AM radio is roughly to Equation Transcription: Text Transcription: (a) {1 over 2} lambda (b) {1 over 4} lambda

How large an emf (rms) will be generated in an antenna that consists of a 380 -loop circular coil of wire in diameter if the EM wave has a frequency of and is transporting energy at an average rate of \(1.0 \times 10^{-4} \mathrm{~W} / \mathrm{m}^{2}\) at the antenna? [Hint: you can use Eq. 21-5 for a generator, since it could be applied to an observer moving with the coil so that the magnetic field is oscillating with the frequency \(f=\omega / 2 \pi\).] Equation Transcription: Text Transcription: 1.0x10^-4 W/m^2 f={omega}/2{pi}

The average intensity of a particular TV station's signal is \(1.0 \times 10^{-13} \mathrm{~W} / \mathrm{m}^2\) when it arrives at a 33 -cm-diameter satellite TV antenna. (a) Calculate the total energy received by the antenna during 6.0 hours of viewing this station's programs. (b) What are the amplitudes of the E and B fields of the EM wave?

Problem 48GP 15 km from a radio station’s transmitting antenna, the amplitude of the electric field is 0.12 V/m. What is the average power output of the radio station?

The variable capacitance of a radio tuner consists of six plates connected together placed alternately between six other plates, also connected together (Fig. 22-21). Each plate is separated from its neighbor by 1.1 mm of air. One set of plates can move so that the area of overlap varies from \(1.0~\mathrm{cm^2}\) to \(9.0~\mathrm{cm^2}\). (a) Are these capacitors connected in series or in parallel? (b) Determine the range of capacitance values. (c) What value of inductor is needed if the radio is to tune AM stations from 550 kHz to 1600 kHz?

Suppose a 50-kW radio station emits EM waves uniformly in all directions. (a) How much energy per second crosses a 1.0-\(\mathrm {m^2}\) area from the transmitting antenna? What is the rms magnitude of the \(\mathrm {\vec E}\) field at this point, assuming the station is operating at full power? (c) What is the voltage induced in a 1.0-m-long vertical car antenna at this distance? Equation Transcription: Text Transcription: m^2 vec{E}

Repeat Problem 52 for a distance of 100 km from the station.

What is the maximum power level of the radio station of Problem 52 so as to avoid electrical breakdown of air at a distance of 1.0 m from the antenna? Assume the antenna is a point source. Air breaks down in an electric field of about \(3 \times 10^{6} \mathrm{~V} / \mathrm{m}\). [Hint: see Problem 51.] Equation Transcription: Text Transcription: 3x10^6 V/m