Physics

Alan Giambattista, Betty McCarthy Richardson, Robert C. Richardson

Chapter 22

Electromagnetic Waves - all with Video Answers

Educators

Chapter Questions

Problem 1

Apply the Ampère-Maxwell law to one of the circular paths in Fig. 22.3 to find the magnitude of the magnetic field at the locations specified.Find $B$ outside the wire at a distance $r \geq R$ from the central axis. [Hint: The electric field inside the wire is constant, so there is no changing electric flux.]

Mayukh Banik

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Problem 2

Apply the Ampère-Maxwell law to one of the circular paths in Fig. 22.3 to find the magnitude of the magnetic field at the locations specified.Find $B$ outside the gap in the wire at a distance $r \geq R$ from the central axis. [Hint: What is the rate of change of electric flux through the circle in terms of the current $I ?]$

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Problem 3

Apply the Ampère-Maxwell law to one of the circular paths in Fig. 22.3 to find the magnitude of the magnetic field at the locations specified.Find $B$ inside the gap in the wire at a distance $r \leq R$ from the central axis. [Hint: Only the rate of change of electric flux $\Delta \Phi_{\mathrm{E}} / \Delta t$ through the interior of the circular path goes into the Ampère-Maxwell law.]

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Problem 4

Apply the Ampère-Maxwell law to one of the circular paths in Fig. 22.3 to find the magnitude of the magnetic field at the locations specified.Find $B$ inside the wire at a distance $r \leq R$ from the central axis. [Hint: Only the current through the interior of the circular path goes into the Ampère-Maxwell law.]

Mayukh Banik

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Problem 5

An electric dipole antenna used to transmit radio waves is oriented vertically.At a point due south of the transmitter, what is the direction of the wave's magnetic field?

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Problem 6

An electric dipole antenna used to transmit radio waves is oriented vertically.At a point due south of the transmitter, what is the direction of the wave's magnetic field?

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Problem 7

An electric dipole antenna used to transmit radio waves is oriented vertically.At a point due north of the transmitter, how should a magnetic dipole antenna be oriented to serve as a receiver?

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Problem 8

An electric dipole antenna used to transmit radio waves is oriented horizontally north-south.At a point due east of the transmitter, what is the direction of the wave's electric field?

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Problem 9

An electric dipole antenna used to transmit radio waves is oriented horizontally north-south.At a point due east of the transmitter, how should a magnetic dipole antenna be oriented to serve as a receiver?

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Problem 10

Using Faraday's law, show that if a magnetic dipole antenna's axis makes an angle $\theta$ with the magnetic field of an EM wave, the induced emf in the antenna is reduced from its maximum possible value by a factor of cos $\theta .$ [Hint: Assume that, at any instant, the magnetic field everywhere inside the loop is uniform. $]$

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Problem 11

A magnetic dipole antenna is used to detect an electromagnetic wave. The antenna is a coil of 50 turns with radius $5.0 \mathrm{cm} .$ The EM wave has frequency $870 \mathrm{kHz}$ electric field amplitude $0.50 \mathrm{V} / \mathrm{m},$ and magnetic field amplitude $1.7 \times 10^{-9} \mathrm{T} .$ (a) For best results, should the axis of the coil be aligned with the electric field of the wave, or with the magnetic field, or with the direction of propagation of the wave? (b) Assuming it is aligned correctly, what is the amplitude of the induced emf in the coil? (Since the wavelength of this wave is much larger than $5.0 \mathrm{cm},$ it can be assumed that at any instant the fields are uniform within the coil.) (c) What is the amplitude of the emf induced in an electric dipole antenna of length $5.0 \mathrm{cm}$ aligned with the electric field of the wave?

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Problem 12

What is the wavelength of the radio waves broadcast by an FM radio station with a frequency of 90.9 MHz?

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Problem 13

What is the frequency of the microwaves in a microwave oven? The wavelength is $12 \mathrm{cm}$

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Problem 14

What is the speed of light in a diamond that has an index of refraction of $2.4168 ?$

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Problem 15

The speed of light in topaz is $1.85 \times 10^{8} \mathrm{m} / \mathrm{s} .$ What is the index of refraction of topaz?

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Problem 16

How long does it take sunlight to travel from the Sun to Earth?

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Problem 17

How long does it take light to travel from this text to your eyes? Assume a distance of $50.0 \mathrm{cm}$.

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Problem 18

The index of refraction of water is $1.33 .$ (a) What is the speed of light in water? (b) What is the wavelength in water of a light wave with a vacuum wavelength of $515 \mathrm{nm} ?$

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Problem 19

Light of wavelength 692 nm in air passes into window glass with an index of refraction of $1.52 .$ (a) What is the wavelength of the light inside the glass? (b) What is the frequency of the light inside the glass?

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Problem 20

How far does a beam of light travel in 1 ns?

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Problem 21

The currents in household wiring and power lines alternate at a frequency of $60.0 \mathrm{Hz}$. (a) What is the wavelength of the EM waves emitted by the wiring?
(b) Compare this wavelength with Earth's radius. (c) In what part of the EM spectrum are these waves?

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Problem 22

In order to study the structure of a crystalline solid, you want to illuminate it with EM radiation whose wavelength is the same as the spacing of the atoms in the crystal $(0.20 \mathrm{nm}) .$ (a) What is the frequency of the EM radiation? (b) In what part of the EM spectrum (radio, visible, etc. $)$ does it lie?

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Problem 23

In musical acoustics, a frequency ratio of 2: 1 is called an octave. Humans with extremely good hearing can hear sounds ranging from $20 \mathrm{Hz}$ to $20 \mathrm{kHz}$, which is approximately 10 octaves (since $2^{10}=1024 \approx 1000$ ).
(a) Approximately how many octaves of visible light are humans able to perceive?
(b) Approximately how many octaves wide is the microwave region?

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Problem 24

You and a friend are sitting in the outfield bleachers of a major league baseball park, 140 m from home plate on a day when the temperature is $20^{\circ} \mathrm{C}$. Your friend is listening to the radio commentary with headphones while watching. The broadcast network has a microphone located $17 \mathrm{m}$ from home plate to pick up the sound as the bat hits the ball. This sound is transferred as an EM wave a distance of $75,000 \mathrm{km}$ by satellite from the ball park to the radio. (a) When the batter hits a hard line drive, who will hear the "crack" of the bat first, you or your friend, and what is the shortest time interval between the bat hitting the ball and one of you hearing the sound? (b) How much later does the other person hear the sound?

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Problem 25

In the United States, the ac household current oscillates at a frequency of $60 \mathrm{Hz}$. In the time it takes for the current to make one oscillation, how far has the electromagnetic wave traveled from the current carrying wire? This distance is the wavelength of a $60-\mathrm{Hz}$ EM wave. Compare this length with the distance from Boston to Los Angeles $(4200 \mathrm{km})$.

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Problem 26

By expressing $\epsilon_{0}$ and $\mu_{0}$ in base SI units $(\mathrm{kg}, \mathrm{m}, \mathrm{s}, \mathrm{A})$ prove that the only combination of the two with dimensions of speed is $\left(\boldsymbol{\epsilon}_{0} \mu_{0}\right)^{-1 / 2}$.

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Problem 27

The electric field in a microwave traveling through air has amplitude $0.60 \mathrm{mV} / \mathrm{m}$ and frequency $30 \mathrm{GHz}$. Find the amplitude and frequency of the magnetic field.

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Problem 28

The magnetic field in a microwave traveling through vacuum has amplitude $4.00 \times 10^{-11} \mathrm{T}$ and frequency $120 \mathrm{GHz}$. Find the amplitude and frequency of the electric field.

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Problem 29

The magnetic field in a radio wave traveling through air has amplitude $2.5 \times 10^{-11} \mathrm{T}$ and frequency $3.0 \mathrm{MHz}$. (a) Find the amplitude and frequency of the electric field. (b) The wave is traveling in the $-y$ -direction. At $y=0$ and $t=0$, the magnetic field is $1.5 \times 10^{-11} \mathrm{T}$ in the $+z$ -direction. What are the magnitude and direction of the electric field at $y=0$ and $t=0 ?$

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Problem 30

The electric field in a radio wave traveling through vacuum has amplitude $2.5 \times 10^{-4} \mathrm{V} / \mathrm{m}$ and frequency $1.47 \mathrm{MHz}$.
(a) Find the amplitude and frequency of the magnetic field. (b) The wave is traveling in the $+x$ -direction. At $x=0$ and $t=0,$ the electric field is $1.5 \times 10^{-4} \mathrm{V} / \mathrm{m}$ in the
- y-direction. What are the magnitude and direction of the magnetic field at $x=0$ and $t=0 ?$.

Mayukh Banik

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Problem 31

The magnetic field of an EM wave is given by $B_{y}=$ $B_{\mathrm{m}} \sin (k z+\omega t), B_{x}=0,$ and $B_{z}=0 .$ (a) In what direction is this wave traveling? (b) Write expressions for the components of the electric field of this wave.

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Problem 32

The electric field of an EM wave is given by $E_{z}=$ $E_{\mathrm{m}} \sin (k y-\omega t+\pi / 6), E_{x}=0,$ and $E_{z}=0 .$ (a) In what direction is this wave traveling? (b) Write expressions for the components of the magnetic field of this wave.

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Problem 33

An EM wave is generated by a magnetic dipole antenna as shown in the figure with Conceptual Question 9. The current in the antenna is produced by an $L C$ resonant circuit. The wave is detected at a distant point $P$. Using the coordinate system in the figure, write equations for the $x-y-$ and $z$ -components of the EM fields at a distant point $P$. (If there is more than one possibility, just give one consistent set of answers.) Define all quantities in your equations in terms of $L, C, E_{m}$ (the electric field amplitude at point $P$ ), and universal constants.

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Problem 34

The intensity of the sunlight that reaches Earth's upper atmosphere is approximately $1400 \mathrm{W} / \mathrm{m}^{2} .$ (a) What is the average energy density? (b) Find the rms values of the electric and magnetic fields.

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Problem 35

The cylindrical beam of a 10.0 -mW laser is $0.85 \mathrm{cm}$ in diameter. What is the rms value of the electric field?

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Problem 36

In astronomy it is common to expose a photographic plate to a particular portion of the night sky for quite some time in order to gather plenty of light. Before leaving a plate exposed to the night sky, Matt decides to test his technique by exposing two photographic plates in his lab to light coming through several pinholes. The source of light is $1.8 \mathrm{m}$ from one photographic plate and the exposure time is $1.0 \mathrm{h}$. For how long should Matt expose a second plate located $4.7 \mathrm{m}$ from the source if the second plate is to have equal exposure (that is, the same energy collected)?

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Problem 37

A $1.0-\mathrm{m}^{2}$ solar panel on a satellite that keeps the panel oriented perpendicular to radiation arriving from the Sun absorbs $1.4 \mathrm{kJ}$ of energy every second. The satellite is located at $1.00 \mathrm{AU}$ from the Sun. (The Earth Sun distance is defined to be $1.00 \mathrm{AU} .$. How long would it take an identical panel that is also oriented perpendicular to the incoming radiation to absorb the same amount of energy, if it were on an interplanetary exploration vehicle 1.55 AU from the Sun? ( W) tutorial: sunlight on Io).

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Problem 38

Fernando detects the electric field from an isotropic source that is $22 \mathrm{km}$ away by tuning in an electric field with an rms amplitude of $55 \mathrm{mV} / \mathrm{m} .$ What is the average power of the source?

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Problem 39

A certain star is 14 million light-years from Earth. The intensity of the light that reaches Earth from the star is $4 \times 10^{-21} \mathrm{W} / \mathrm{m}^{2} .$ At what rate does the star radiate EM energy?

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Problem 40

The intensity of the sunlight that reaches Earth's upper atmosphere is approximately $1400 \mathrm{W} / \mathrm{m}^{2} .$ (a) What is the total average power output of the Sun, assuming it to be an isotropic source? (b) What is the intensity of sunlight incident on Mercury, which is $5.8 \times 10^{10} \mathrm{m}$ from the Sun?

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Problem 41

Prove that, in an EM wave traveling in vacuum, the electric and magnetic energy densities are equal; that is, prove that,$$\frac{1}{2} \epsilon_{0} E^{2}=\frac{1}{2 \mu_{0}} B^{2}$$ at any point and at any instant of time.,

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Problem 42

Verify that the equation $I=\langle u\rangle c$ is dimensionally consistent (i.e., check the units).

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Problem 43

The solar panels on the roof of a house measure $4.0 \mathrm{m}$ by $6.0 \mathrm{m} .$ Assume they convert $12 \%$ of the incident EM wave's energy to electric energy. (a) What average power do the panels supply when the incident intensity is $1.0 \mathrm{kW} / \mathrm{m}^{2}$ and the panels are perpendicular to the incident light? (b) What average power do the panels supply when the incident intensity is $0.80 \mathrm{kW} / \mathrm{m}^{2}$ and the light is incident at an angle of $60.0^{\circ}$ from the normal? (W) tutorial: solar collector) (c) Take the average daytime power requirement of a house to be about 2 kW. How do your answers to (a) and (b) compare? What are the implications for the use of solar panels?

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Problem 44

The radio telescope in Arecibo, Puerto Rico, has a diameter of $305 \mathrm{m}$. It can detect radio waves from space with intensities as small as $10^{-26} \mathrm{W} / \mathrm{m}^{2} .$ (a) What is the average power incident on the telescope due to a wave at normal incidence with intensity $1.0 \times 10^{-26} \mathrm{W} / \mathrm{m}^{2} ?$ (b) What is the average power incident on Earth's surface? (c) What are the rms electric and magnetic fields?

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Problem 45

Unpolarized light passes through two polarizers in turn with polarization axes at $45^{\circ}$ to one another.What is the fraction of the incident light intensity that is transmitted?

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Problem 46

Light polarized in the $x$ -direction shines through two polarizing sheets. The first sheet's transmission axis makes an angle $\theta$ with the $x$ -axis and the transmission axis of the second is parallel to the $y$ -axis. (a) If the incident light has intensity $I_{0},$ what is the intensity of the light transmitted through the second sheet? (b) At what angle $\theta$ is the transmitted intensity maximum?

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Problem 47

Unpolarized light is incident on a system of three polarizers. The second polarizer is oriented at an angle of $30.0^{\circ}$ with respect to the first and the third is oriented at an angle of $45.0^{\circ}$ with respect to the first. If the light that emerges from the system has an intensity of $23.0 \mathrm{W} / \mathrm{m}^{2},$ what is the intensity of the incident light?

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Problem 48

Unpolarized light is incident on four polarizing sheets with their transmission axes oriented as shown in the figure. What percentage of the initial light intensity is transmitted through this set of polarizers?

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Problem 49

A polarized beam of light has intensity $I_{0} .$ We want to rotate the direction of polarization by $90.0^{\circ}$ using polarizing sheets. (a) Explain why we must use at least two sheets. (b) What is the transmitted intensity if we use two sheets, each of which rotates the direction of polarization by $45.0^{\circ} ?$ (c) What is the transmitted intensity if we use four sheets, each of which rotates the direction of polarization by $22.5^{\circ} ?$

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Problem 50

Vertically polarized microwaves traveling into the page are directed at each of three metal plates $(a, b, c)$ that have parallel slots cut in them. (a) Which plate transmits microwaves best? (b) Which plate reflects microwaves best? (c) If the intensity transmitted through the best transmitter is $I_{1},$ what is the intensity transmitted through the second-best transmitter?

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Problem 51

Two sheets of polarizing material are placed with their transmission axes at right angles to one another. A third polarizing sheet is placed between them with its transmission axis at $45^{\circ}$ to the axes of the other two. (a) If unpolarized light of intensity $I_{0}$ is incident on the system, what is the intensity of the transmitted light?(b) What is the intensity of the transmitted light when

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Problem 52

Vertically polarized light with intensity $I_{0}$ is normally incident on an ideal polarizer. As the polarizer is rotated about a horizontal axis, the intensity $I$ of light transmitted through the polarizer varies with the orientation of the polarizer $(\theta),$ where $\theta=0$ corresponds to a vertical transmission axis. Sketch a graph of $I$ as a function of $\theta$ for one complete rotation of the polarizer $\left(0 \leq \theta \leq 360^{\circ}\right)$.(W) tutorial: polarized light).

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Problem 53

Just after sunrise, you look north at the sky just above the horizon. Is the light you see polarized? If so, in what direction?

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Problem 54

Just after sunrise, you look straight up at the sky. Is the light you see polarized? If so, in what direction?

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Problem 55

If the speeder in Example 22.9 were going faster than the police car, how fast would it have to go so that the reflected microwaves produce the same number of beats per second?

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Problem 56

Light of wavelength $659.6 \mathrm{nm}$ is emitted by a star. The wavelength of this light as measured on Earth is $661.1 \mathrm{nm} .$ How fast is the star moving with respect to Earth? Is it moving toward Earth or away from it?

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Problem 57

A star is moving away from Earth at a speed of $2.4 \times 10^{8} \mathrm{m} / \mathrm{s} .$ Light of wavelength $480 \mathrm{nm}$ is emitted by the star. What is the wavelength as measured by an Earth observer?

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Problem 58

A police car's radar gun emits microwaves with a frequency of $f_{1}=7.50 \mathrm{GHz}$. The beam reflects from a speeding car, which is moving toward the police car at $48.0 \mathrm{m} / \mathrm{s}$ with respect to the police car. The speeder's radar detector detects the microwave at a frequency $f_{2}$.
(a) Which is larger, $f_{1}$ or $f_{2} ?$ (b) Find the frequency difference $f_{2}-f_{1}$.

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Problem 59

A police car's radar gun emits microwaves with a frequency of $f_{1}=36.0 \mathrm{GHz}$. The beam reflects from a speeding car, which is moving away at $43.0 \mathrm{m} / \mathrm{s}$ with respect to the police car. The frequency of the reflected microwave as observed by the police is $f_{2} .$ (a) Which is larger, $f_{1}$ or $f_{2} ?$ (b) Find the frequency difference $f_{2}-f_{1}$ [Hint: There are two Doppler shifts. First think of the police as source and the speeder as observer. The speeding car "retransmits" a reflected wave at the same frequency at which it observes the incident wave. $]$

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Problem 60

What must be the relative speed between source and receiver if the wavelength of an EM wave as measured by the receiver is twice the wavelength as measured by the source? Are source and observer moving closer together or farther apart?

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Problem 61

How fast would you have to drive in order to see a red light as green? Take $\lambda=630$ nm for red and $\lambda=530 \mathrm{nm}$ for green.

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Problem 62

Calculate the frequency of an EM wave with a wavelength the size of (a) the thickness of a piece of paper $(60 \mu \mathrm{m}),(\mathrm{b})$ a $91-\mathrm{m}$ -long soccer field, (c) the diameter of Earth, (d) the distance from Earth to the Sun.

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Problem 63

The intensity of solar radiation that falls on a detector on Earth is $1.00 \mathrm{kW} / \mathrm{m}^{2} .$ The detector is a square that measures $5.00 \mathrm{m}$ on a side and the normal to its surface makes an angle of $30.0^{\circ}$ with respect to the Sun's radiation. How long will it take for the detector to measure
$420 \mathrm{kJ}$ of energy?

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Problem 64

Astronauts on the Moon communicated with mission control in Houston via EM waves. There was a noticeable time delay in the conversation due to the round-trip transit time for the EM waves between the Moon and the Earth. How long was the time delay?

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Problem 65

The antenna on a cordless phone radiates microwaves at a frequency of $2.0 \mathrm{GHz}$. What is the maximum length of the antenna if it is not to exceed half of a wavelength?

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Problem 66

Two identical television signals are sent between two cities that are $400.0 \mathrm{km}$ apart. One signal is sent through the air, and the other signal is sent through a fiber optic network. The signals are sent at the same time but the one traveling through air arrives $7.7 \times 10^{-4}$ s before the one traveling through the glass fiber. What is the index of refraction of the glass fiber?

Susan Hallstrom

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Problem 67

An AM radio station broadcasts at $570 \mathrm{kHz}$. (a) What is the wavelength of the radio wave in air? (b) If a radio is tuned to this station and the inductance in the tuning circuit is $0.20 \mathrm{mH},$ what is the capacitance in the tuning circuit? (c) In the vicinity of the radio, the amplitude of the electric field is $0.80 \mathrm{V} / \mathrm{m} .$ The radio uses a coil antenna of radius $1.6 \mathrm{cm}$ with 50 turns. What is the maximum emf induced in the antenna, assuming it is oriented for best reception? Assume that the fields are sinusoidal functions of time.

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Problem 68

A 60.0 -m $\mathrm{W}$ pulsed laser produces a pulse of EM radia tion with wavelength $1060 \mathrm{nm}$ (in air) that lasts for 20.0 ps (picoseconds). (a) In what part of the EM spectrum is this pulse? (b) How long (in centimeters) is :
single pulse in air? (c) How long is it in water $(n=1.33) \equiv$
(d) How many wavelengths fit in one pulse? (e) What is the total electromagnetic energy in one pulse?

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Problem 69

The range of wavelengths allotted to the radio broadcast band is from about $190 \mathrm{m}$ to $550 \mathrm{m} .$ If each station needs exclusive use of a frequency band $10 \mathrm{kHz}$ wide, how many stations can operate in the broadcast band?

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Problem 70

Polarized light of intensity $I_{0}$ is incident on a pair of polarizing sheets. Let $\theta_{1}$ and $\theta_{2}$ be the angles between the direction of polarization of the incident light and the transmission axes of the first and second sheets, respectively. Show that the intensity of the transmitted light is $I=I_{0} \cos ^{2} \theta_{1} \cos ^{2}\left(\theta_{1}-\theta_{2}\right)$.

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Problem 71

An unpolarized beam of light (intensity $I_{0}$ ) is moving in the $x$ -direction. The light passes through three ideal polarizers whose transmission axes are (in order) at angles $0.0^{\circ}, 45.0^{\circ},$ and $30.0^{\circ}$ counterclockwise from the $y$ -axis in the $y z$ -plane. (a) What is the intensity and polarization of the light that is transmitted by the last polarizer? (b) If the polarizer in the middle is removed, what is the intensity and polarization of the light transmitted by the last polarizer?

Mayukh Banik

Numerade Educator

Problem 72

What are the three lowest angular speeds for which the wheel in Fizeau's apparatus (see Fig. 22.13 ) allows the reflected light to pass through to the observer? Assume the distance between the notched wheel and the mirror is $8.6 \mathrm{km}$ and that there are 5 notches in the wheel.

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Problem 73

A microwave oven can heat 350 g of water from $25.0^{\circ} \mathrm{C}$ to $100.0^{\circ} \mathrm{C}$ in 2.00 min. (a) At what rate is energy absorbed by the water? (b) Microwaves pass through a waveguide of cross-sectional area $88.0 \mathrm{cm}^{2} .$ What is the average intensity of the microwaves in the wave guide?
(c) What are the rms electric and magnetic fields inside the wave guide?

Mayukh Banik

Numerade Educator

Problem 74

A sinusoidal EM wave has an electric field amplitude $E_{\mathrm{m}}=32.0 \mathrm{mV} / \mathrm{m} .$ What are the intensity and average energy density? [Hint: Recall the relationship between amplitude and rms value for a quantity that varies sinusoidally.]

Mayukh Banik

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Problem 75

Energy carried by an EM wave coming through the air can be used to light a bulb that is not connected to a battery or plugged into an electric outlet. Suppose a receiving antenna is attached to a bulb and the bulb is found to dissipate a maximum power of 1.05 W when the antenna is aligned with the electric field coming from a distant source. The wavelength of the source is large compared to the antenna length. When the antenna is rotated so it makes an angle of $20.0^{\circ}$ with the incoming electric field, what is the power dissipated by the bulb?

Mayukh Banik

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Problem 76

A $10-$ W laser emits a beam of light 4.0 mm in diameter. The laser is aimed at the Moon. By the time it reaches the Moon, the beam has spread out to a diameter of $85 \mathrm{km} .$ Ignoring absorption by the atmosphere, what is the intensity of the light (a) just outside the laser and (b) where it hits the surface of the Moon?

Mayukh Banik

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Problem 77

To measure the speed of light, Galileo and a colleague stood on different mountains with covered lanterns. Galileo uncovered his lantern and his friend, seeing the light, uncovered his own lantern in turn. Galileo measured the elapsed time from uncovering his lantern to seeing the light signal response. The elapsed time should be the time for the light to make the round trip plus the reaction time for his colleague to respond. To determine reaction time, Galileo repeated the experiment while he and his friend were close to one another. He found the same time whether his colleague was nearby or far away and concluded that light traveled almost instantaneously. Suppose the reaction time of Galileo's colleague was $0.25 \mathrm{s}$ and for Galileo to observe a difference, the complete round trip would have to take 0.35 s. How far apart would the two mountains have to be for Galileo to observe a finite speed of light? Is this feasible?

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Problem 78

Suppose some astronauts have landed on Mars. (a) When Mars and Earth are on the same side of the Sun and as close as they can be to one another, how long does it take for radio transmissions to travel one way between the two planets? (b) Suppose the astronauts ask a question of mission control personnel on Earth. What is the shortest possible time they have to wait for a response? The average distance from Mars to the Sun is $2.28 \times 10^{11} \mathrm{m}$.

Mayukh Banik

Numerade Educator