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physics scientists and engineers

Physics for Scientists and Engineers A Strategic Approach with Modern Physics 4th edition Randall D. Knight - Solutions

An underwater diver sees the sun 50° above horizontal. How high is the sun above the horizon to a fisherman in a boat above the diver?
A costume jewelry pendant made of cubic zirconia is submerged in oil. A light ray strikes one face of the zirconia crystal at an angle of incidence of 25°. Once inside, what is the ray’s angle with respect to the face of the crystal?
A 1.0-cm-thick layer of water stands on a horizontal slab of glass. A light ray in the air is incident on the water 60° from the normal. What is the ray’s direction of travel in the glass?
A laser beam in air is incident on a liquid at an angle of 53° with respect to the normal. The laser beam’s angle in the liquid is 35°. What is the liquid’s index of refraction?
When you look at your reflection in the bowl of a spoon, it is upside down. Why?
You see an upright, magnified image of your face when you look into a magnifying cosmetic mirror. Where is the image? Is it in front of the mirror’s surface, on the mirror’s surface, or behind the mirror’s surface? Explain.
It is 165 cm from your eyes to your toes. You’re standing 200 cm in front of a tall mirror. How far is it from your eyes to the image of your toes?
A concave mirror brings the sun’s rays to a focus in front of the mirror. Suppose the mirror is submerged in a swimming pool but still pointed up at the sun. Will the sun’s rays be focused nearer to, farther from, or at the same distance from the mirror? Explain.
A laser beam is incident on the left mirror in FIGURE EX34.8. Its initial direction is parallel to a line that bisects the mirrors.What is the angle Ï• of the reflected laser beam? 80° FIGURE EX34.8
A converging lens creates the image shown in FIGURE Q34.8. Is the object distance less than the focal length f, between f and 2f, or greater than 2f? Explain. FIGURE Q34.8
At what angle Ï• should the laser beam in FIGURE EX34.7 be aimed at the mirrored ceiling in order to hit the midpoint of the far wall? Mirror 3.0 m Wall Laser beam FIGURE EX34.7 5.0 m
The object and lens in FIGURE Q34.7 are positioned to form a well-focused, inverted image on a viewing screen. Then a piece of cardboard is lowered just in front of the lens to cover the top half of the lens. Describe what you see on the screen when the cardboard is in place. Screen FIGURE Q34.7
The mirror in FIGURE EX34.6 deflects a horizontal laser beam by 60°. What is the angle Ï•? 60° FIGURE EX34.6
Consider one point on an object near a lens.a. What is the minimum number of rays needed to locate its image point? Explain.b. How many rays from this point actually strike the lens and refract to the image point?
A light ray leaves point A in FIGURE EX34.5, reflects from the mirror, and reaches point B. How far below the top edge does the ray strike the mirror? 5 cm 10 cm A Mirror 15 cm 15 cm FIGURE EX34.5
A fish in an aquarium with flat sides looks out at a hungry cat. To the fish, does the distance to the cat appear to be less than the actual distance, the same as the actual distance, or more than the actual distance? Explain.
A 5.0-cm-thick layer of oil is sandwiched between a 1.0-cm-thick sheet of glass and a 2.0-cm-thick sheet of polystyrene plastic. How long (in ns) does it take light incident perpendicular to the glass to pass through this 8.0-cm-thick sandwich?
A light beam passing from medium 2 to medium 1 is refracted as shown in FIGURE Q34.4. Is n1larger than n2, is n1smaller than n2, or is there not enough information to tell? Explain. 1 2.
A student has built a 15-cm-long pinhole camera for a science fair project. She wants to photograph her 180-cm tall friend and have the image on the film be 5.0 cm high. How far should the front of the camera be from her friend?
One problem with using optical fibers for communication is that a light ray passing directly down the center of the fiber takes less time to travel from one end to the other than a ray taking a longer, zig-zag path. Thus light rays starting at the same time but traveling in slightly different
a. How long (in ns) does it take light to travel 1.0 m in vacuum?b. What distance does light travel in water, glass, and cubic zirconia during the time that it travels 1.0 m in vacuum?
You are looking at the image of a pencil in a mirror, as shown in FIGURE Q34.2. a. What happens to the image if the top half of the mirror, down to the midpoint, is covered with a piece of cardboard? Explain.b. What happens to the image if the bottom half of the mirror is covered with a piece of
A point source of light illuminates an aperture 2.0 m away. A 12.0-cm-wide bright patch of light appears on a screen 1.0 m behind the aperture. How wide is the aperture?
Is the electric field strength in FIGURE Q31.5 increasing, decreasing, or not changing? Explain. Induced B FIGURE Q31.5
The intensity of an electromagnetic wave is 10 W/m2. What will the intensity be if:a. The amplitude of the electric field is doubled?b. The amplitude of the magnetic field is doubled?c. The amplitudes of both the electric and the magnetic fields are doubled?d. The frequency is doubled?
What capacitance, in цF, has its potential difference increasing at 1.0 × 106 V/s when the displacement current in the capacitor is 1.0 A?
A series RL circuit is built with a 110 Ω resistor and a 5.0-cm long, 1.0-cm-diameter solenoid with 800 turns of wire. What is the peak magnetic flux through the solenoid if the circuit is driven by a 12 V, 5.0 kHz source?
A proton is fired with a speed of 1.0 × 106m/s through the parallel-plate capacitor shown in FIGURE P31.31. The capacitor??s electric field is E = (1.0 × 105V/m, down). a. What magnetic field B, both strength and direction, must be applied to allow the proton to pass through the capacitor with
What electric field strength and direction will allow the proton in FIGURE P31.30 to pass through this region of space without being deflected? B= 0.010 T- v = 2.0 x 107 m/s FIGURE P31.30 +
What is the force (magnitude and direction) on the proton in FIGURE P31.29? Give the direction as an angle cw or ccw from vertical. E= 1.0 x 10 V/m x / x v = 1.0 x 10' m/s B= 0.10 T FIGURE P31.29
What are the electric field strength and direction at the position of the electron in FIGURE P31.28 ? 3.2 x 10-13 N F 30° B=0.10 T Moving out of page at 1.0 x 10' m/s FIGURE P31.28
A 200 mW vertically polarized laser beam passes through a polarizing filter whose axis is 35° from horizontal. What is the power of the laser beam as it emerges from the filter?
Unpolarized light with intensity 350 W/m2 passes first through a polarizing filter with its axis vertical, then through a second polarizing filter. It emerges from the second filter with intensity 131 W/m2. What is the angle from vertical of the axis of the second polarizing filter?
FIGURE EX31.25 shows a vertically polarized radio wave of frequency 1.0 × 106Hz traveling into the page.The maximum electric field strength is 1000 V/m. What are a. The maximum magnetic field strength?b. The magnetic field strength and direction at a point where E = (500 V/m, down)? y E -
Only 25% of the intensity of a polarized light wave passes through a polarizing filter. What is the angle between the electric field and the axis of the filter?
At what distance from a 10 W point source of electromagnetic waves is the magnetic field amplitude 1.0 μT?
A 1000 W carbon-dioxide laser emits light with a wavelength of 10 μm into a 3.0-mm-diameter laser beam. What force does the laser beam exert on a completely absorbing target?
A 200 MW laser pulse is focused with a lens to a diameter of 2.0 μm.a. What is the laser beam’s electric field amplitude at the focal point?b. What is the ratio of the laser beam’s electric field to the electric field that keeps the electron bound to the proton of a hydrogen atom? The radius
A radio antenna broadcasts a 1.0 MHz radio wave with 25 kW of power. Assume that the radiation is emitted uniformly in all directions.a. What is the wave’s intensity 30 km from the antenna?b. What is the electric field amplitude at this distance?
A helium-neon laser emits a 1.0-mm-diameter laser beam with a power of 1.0 mW. What are the amplitudes of the electric and magnetic fields of the light wave?
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 radio wave is traveling in the negative y-direction. What is the direction of E at a point where B is in the positive x direction?
a. What is the magnetic field amplitude of an electromagnetic wave whose electric field amplitude is 100 V/m?b. What is the intensity of the wave?
The electric field of an electromagnetic wave in a vacuum is Ey = (20.0 V/m) cos [(6.28 × 108)x - ωt], where x is in m and t is in s. What are the wave’s(a) Wavelength,(b) Frequency,(c) Magnetic field amplitude?
The magnetic field of an electromagnetic wave in a vacuum is Bz = (3.00 μT) sin [( 1.00 × 107)x - ωt], where x is in m and t is in s. What are the wave’s(a) Wavelength,(b) Frequency,(c) Electric field amplitude?
What is the electric field amplitude of an electromagnetic wave whose magnetic field amplitude is 2.0 mT?
What is the magnetic field amplitude of an electromagnetic wave whose electric field amplitude is 10 V/m?
A 10-cm-diameter parallel-plate capacitor has a 1.0 mm spacing. The electric field between the plates is increasing at the rate 1.0 × 106 V/m s. What is the magnetic field strength (a) On the axis,(b) 3.0 cm from the axis,(c) 7.0 cm from the axis?
A 5.0-cm-diameter parallel-plate capacitor has a 0.50 mm gap. What is the displacement current in the capacitor if the potential difference across the capacitor is increasing at 500,000 V/s?
A vertically polarized electromagnetic wave passes through the five polarizers in FIGURE Q31.10. Rank in order, from largest to smallest, the transmitted intensities Iato Ie. P
Older televisions used a loop antenna like the one in FIGURE Q31.9. How does this antenna work?
Show that the displacement current inside a parallel-plate capacitor can be written C(dVC/dt).
Show that the quantity є0(dΦe/dt) has units of current.
In what directions are the electromagnetic waves traveling in FIGURE Q31.7 ? a. b. L Le L Li
The magnetic field is uniform over each face of the box shown in FIGURE EX31.6. What are the magnetic field strength and direction on the front surface? 2T 2T 3 T 3T 1 cm 2 cm FIGURE EX31.6 1 cm 1T
Do the situations in FIGURE Q31.6 represent possible electromagnetic waves? If not, why not? a. b. 3000 V/m Vem 10 μΤy
A rocket zooms past the earth at v = 2.0 × 106m/s. Scientists on the rocket have created the electric and magnetic fields shown in FIGURE EX31.5. What are the fields measured by an earthbound scientist? B = 1.0 T 2.0 x 106 m/s E = 1.0 x 106 V/m FIGURE EX31.5
Scientists in the laboratory create a uniform electric field E =1.0 × 106 kn V/m in a region of space where B = 0. What are the fields in the reference frame of a rocket traveling in the positive x-direction at 1.0 × 106 m/s?
What is the current through surface S in FIGURE Q31.4 if you curl your right fingers in the direction of the arrow? 2 A S 2A FIGURE Q31.4
Laboratory scientists have created the electric and magnetic fields shown in FIGURE EX31.3. These fields are also seen by scientists who zoom past in a rocket traveling in the x-direction at 1.0 × 106m/s. According to the rocket scientists, what angle does the electric field make with the axis of
If you curl the fingers of your right hand as shown, are the electric fluxes in FIGURE Q31.3 positive or negative? a. b. x x x x x х х x x
A rocket cruises past a laboratory at 1.00 × 106 m/s in the positive x-direction just as a proton is launched with velocity (in the laboratory frame) v = (1.41 × 106î + 1.41 × 106ĵ) m/s. What are the proton’s speed and its angle from the y-axis in (a) The laboratory frame(b) The
Sharon drives her rocket through the magnetic field of FIGURE Q31.2 traveling to the right at a speed of 1000 m/s as measured by Bill. As she passes Bill, she shoots a positive charge backward at a speed of 1000 m/s relative to her. a. According to Bill, what kind of force or forces act on the
FIGURE EX31.1 shows the electric and magnetic field in frame A. A rocket in frame B travels parallel to one of the axes of the A coordinate system. Along which axis must the rocket travel, and in which direction, in order for the rocket scientists to measure (a) BB > BA, (b) BB = BA, (c) BB <
Andre is flying his spaceship to the left through the laboratory magnetic field of FIGURE Q31.1. a. Does Andre see a magnetic field? If so, in which direction does it point?b. Does Andre see an electric field? If so, in which direction does it point? Andre FIGURE Q31.1
Let’s look at the details of eddy-current braking. A square loop, length l on each side, is shot with velocity v0 into a uniform magnetic field B. The field is perpendicular to the plane of the loop. The loop has mass m and resistance R, and it enters the field at t = 0 s. Assume that the loop is
A 10 cm × 10 cm square loop lies in the xy-plane. The magnetic field in this region of space is B = (0.30tî + 0.50t2 k̂) T, where t is in s. What is the emf induced in the loop at(a) T = 0.5 s(b) T = 1.0 s?
FIGURE EX30.18 shows the current as a function of time through a 20-cm-long, 4.0-cm-diameter solenoid with 400 turns. Draw a graph of the induced electric field strength as a function of time at a point 1.0 cm from the axis of the solenoid. I (A) 5- 0+ 0.0 0.1 0.2 - (s) 0.4 0.3 0.4 FIGURE EX30.18
A 5.0-cm-diameter coil has 20 turns and a resistance of 0.50 Ω. A magnetic field perpendicular to the coil is B = 0.020t + 0.010t2, where B is in tesla and t is in seconds.a. Find an expression for the induced current I(t) as a function of time.b. Evaluate I at t = 5 s and t = 10 s.
The current in the solenoid of FIGURE EX30.12 is increasing. The solenoid is surrounded by a conducting loop. Is there a current in the loop? If so, is the loop current cw or ccw? FIGURE EX30.12
An electron travels with v = 5.0 × 106î m/s through a point in space where E = (2.0 × 105î - 2.0 × 105ĵ) V/m and B = -0.10k̂ T. What is the force on the electron?
In FIGURE P31.33, a circular loop of radius r travels with speed v along a charged wire having linear charge density λ. The wire is at rest in the laboratory frame, and it passes through the center of the loop. a. What are E and B at a point on the loop as measured by a scientist in the
The magnetic field inside a 4.0-cm-diameter superconducting solenoid varies sinusoidally between 8.0 T and 12.0 T at a frequency of 10 Hz.a. What is the maximum electric field strength at a point 1.5 cm from the solenoid axis?b. What is the value of B at the instant E reaches its maximum value?
A simple series circuit consists of a 150 Ω resistor, a 25 V battery, a switch, and a 2.5 pF parallel-plate capacitor (initially uncharged) with plates 5.0 mm apart. The switch is closed at t = 0 s.a. After the switch is closed, find the maximum electric flux and the maximum displacement current
A wire with conductivity σ carries current I. The current is increasing at the rate dI/dt.a. Show that there is a displacement current in the wire equal to (є0/σ)(dI/dt).b. Evaluate the displacement current for a copper wire in which the current is increasing at 1.0 × 106 A/s.
A 10 A current is charging a 1.0-cm-diameter parallel-plate capacitor.a. What is the magnetic field strength at a point 2.0 mm radially from the center of the wire leading to the capacitor?b. What is the magnetic field strength at a point 2.0 mm radially from the center of the capacitor?
FIGURE P31.38 shows the voltage across a 0.10 μF capacitor. Draw a graph showing the displacement current through the capacitor as a function of time. AVe (V) 100 50- 0+ t (us) FIGURE P31.38 1 3 4 2.
FIGURE P31.39 shows the electric field inside a cylinder of radius R = 3.0 mm. The field strength is increasing with time as E = 1.0 × 108t2V/m, where t is in s. The electric field outside the cylinder is always zero, and the field inside the cylinder was zero for t < 0. a. Find an expression
A long, thin superconducting wire carrying a 15 A current passes through the center of a thin, 2.0-cm-diameter ring. A uniform electric field of increasing strength also passes through the ring, parallel to the wire. The magnetic field through the ring is zero.a. At what rate is the electric field
A 1.0 μF capacitor is discharged, starting at t = 0 s. The displacement current through the plates is Idisp = (10 A)exp(-t/2.0 μs). What was the capacitor’s initial voltage (ΔVC)0?
At one instant, the electric and magnetic fields at one point of an electromagnetic wave are E = (200î + 300ĵ - 50k̂) V/m and B = B0(7.3î - 7.3 ĵ + ak̂) μT.a. What are the values of a and B0?b. What is the Poynting vector at this time and position?
a. Show that uE and uB, the energy densities of the electric and magnetic fields, are equal to each other in an electromagnetic wave. In other words, show that the wave’s energy is divided equally between the electric field and the magnetic field.b. What is the total energy density in an
The intensity of sunlight reaching the earth is 1360 W/m2.a. What is the power output of the sun?b. What is the intensity of sunlight reaching Mars?
Assume that a 7.0-cm-diameter, 100 W lightbulb radiates all its energy as a single wavelength of visible light. Estimate the electric and magnetic field strengths at the surface of the bulb.
The electric field of a 450 MHz radio wave has a maximum rate of change of 4.5 × 1011 (V/m)/s. What is the wave’s magnetic field amplitude?
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 images, broadcast with a mere 21 W of power. Assuming that the transmitter broadcast equally in all directions,a. What signal intensity was received on
In reading the instruction manual that came with your garage-door opener, you see that the transmitter unit in your car produces a 250 mW, 350 MHz signal and that the receiver unit is supposed to respond to a radio wave at this frequency if the electric field amplitude exceeds 0.10 V/m. You wonder
The maximum electric field strength in air is 3.0 MV/m. Stronger electric fields ionize the air and create a spark. What is the maximum power that can be delivered by a 1.0 cm-diameter laser beam propagating through air?
A LASIK vision-correction system uses a laser that emits 10 ns-long pulses of light, each with 2.5 mJ of energy. The laser beam is focused to a 0.85-mm-diameter circle on the cornea.What is the electric field amplitude of the light wave at the cornea?
The intensity of sunlight reaching the earth is 1360 W/m2. Assuming all the sunlight is absorbed, what is the radiation-pressure force on the earth? Give your answer(a) In newtons(b) As a fraction of the sun’s gravitational force on the earth.
For radio and microwaves, the depth of penetration into the human body is proportional to λ1/2. If 27 MHz radio waves penetrate to a depth of 14 cm, how far do 2.4 GHz microwaves penetrate?
A laser beam shines straight up onto a flat, black foil of mass m.a. Find an expression for the laser power P needed to levitate the foil.b. Evaluate P for a foil with a mass of 25 μg.
For a science project, you would like to horizontally suspend an 8.5 by 11 inch sheet of black paper in a vertical beam of light whose dimensions exactly match the paper. If the mass of the sheet is 1.0 g, what light intensity will you need?
You’ve recently read about a chemical laser that generates a 20-cm-diameter, 25 MW laser beam. One day, after physics class, you start to wonder if you could use the radiation pressure from this laser beam to launch small payloads into orbit. To see if this might be feasible, you do a quick
Unpolarized light of intensity I0 is incident on three polarizing filters. The axis of the first is vertical, that of the second is 45° from vertical, and that of the third is horizontal. What light intensity emerges from the third filter?
Unpolarized light of intensity I0 is incident on two polarizing filters. The transmitted light intensity is I0/10. What is the angle between the axes of the two filters?
Unpolarized light of intensity I0 is incident on a stack of 7 polarizing filters, each with its axis rotated 15° cw with respect to the previous filter. What light intensity emerges from the last filter?
A cube of water 10 cm on a side is placed in a microwave beam having E0 = 11 kV/m. The microwaves illuminate one face of the cube, and the water absorbs 80% of the incident energy. How long will it take to raise the water temperature by 50°C? Assume that the water has no heat loss during this time.
An 80 kg astronaut has gone outside his space capsule to do some repair work. Unfortunately, he forgot to lock his safety tether in place, and he has drifted 5.0 m away from the capsule.Fortunately, he has a 1000 W portable laser with fresh batteries that will operate it for 1.0 h. His only chance
An electron travels with v = 5.0 × 106 in m/s through a point in space where B = 0.10 ĵ T. The force on the electron at this point is F = (9.6 × 10-14î - 9.6 × 10-14k̂) N. What is the electric field?

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