An L-R-C series circuit has R = 500 Ω, L = 2.00 H, C = 0.500 µF, and V = 100 V. a. For ω = 800 rad/s, calculate VR, VL, VC, and ɸ. Using a single set of axes, graph v, vR, vL, and vC as functions of time. Include two cycles of v on your graph. b. Repeat part (a) for ω = 1000 rad/s. c. Repeat part (a) for ω = 1250 rad/s.
> The electric field
> Explain this statement: “In a static situation, the electric field at the surface of a conductor can have no component parallel to the surface because this would violate the condition that the charges on the surface are at rest.” Would this statement be
> A very small object with mass 8.20 × 10-9 kg and positive charge 6.50 × 10-9 C is projected directly toward a very large insulating sheet of positive charge that has uniform surface charge density 5.90 × 10-8 C/m2. The object is initially 0.400 m from th
> Two charges are placed on the x-axis: one, of 2.50 µC, at the origin and the other, of -3.50 µC, at x = 0.600 m (Fig. P21.60). Find the position on the x-axis where the net force on a small charge +q would be zero. Fig. P21.60:
> A person who has skin of surface area 1.85 m2 and temperature 30.0°C is resting in an insulated room where the ambient air temperature is 20.0°C. In this state, a person gets rid of excess heat by radiation. By how much does the person change the entropy
> A heat engine operates using the cycle shown in Fig. P20.41. The working substance is 2.00 mol of helium gas, which reaches a maximum temperature of 3270C. Assume the helium can be treated as an ideal gas. Process bc is isothermal. Fig. P20.41: The pr
> As a budding mechanical engineer, you are called upon to design a Carnot engine that has 2.00 mol of a monatomic ideal gas as its working substance and operates from a high temperature reservoir at 5000C. The engine is to lift a 15.0-kg weight 2.00 m per
> You build a heat engine that takes 1.00 mol of an ideal diatomic gas through the cycle shown in Fig. P20.39. Fig. P20.39: (a). Show that process ab is an isothermal compression. (b). During which process(es) of the cycle is heat absorbed by the gas?
> What is the thermal efficiency of an engine that operates by taking n moles of diatomic ideal gas through the cycle 1→ 2→ 3→ 4→ 1 shown in Fig. P20.38? Fig. P20.38: P 2 3 2po P
> Digesting fat produces 9.3 food calories per gram of fat, and typically 80% of this energy goes to heat when metabolized. (One food calorie is 1000 calories and therefore equals 4186 J.) The body then moves all this heat to the surface by a combination o
> A heat engine takes 0.350 mol of a diatomic ideal gas around the cycle shown in the pV-diagram of Fig. P20.36. Process 1→ 2 is at constant volume, process 2→ 3 is adiabatic, and process 3→ 1 is at a c
> A certain heat engine operating on a Carnot cycle absorbs 410 J of heat per cycle at its hot reservoir at 135°C and has a thermal efficiency of 22.0%. (a). How much work does this engine do per cycle? (b). How much heat does the engine waste each cycle
> A solid conductor has a cavity in its interior. Would the presence of a point charge inside the cavity affect the electric field outside the conductor? Why or why not? Would the presence of a point charge outside the conductor affect the electric field i
> An average sleeping person metabolizes at a rate of about 80 W by digesting food or burning fat. Typically, 20% of this energy goes into bodily functions, such as cell repair, pumping blood, and other uses of mechanical energy, while the rest goes to hea
> A small sphere with mass 4.00 × 10-6 kg and charge 5.00 × 10-8 C hangs from a thread near a very large, charged insulating sheet (Fig. P22.33). The charge density on the surface of the sheet is uniform and equal to -2.50 Ã
> You are designing a Carnot engine that has 2 mol of CO2 as its working substance; the gas may be treated as ideal. The gas is to have a maximum temperature of 527sC and a maximum pressure of 5.00 atm. With a heat input of 400 J per cycle, you want 300 J
> At time t = 0 a proton is a distance of 0.360 m from a very large insulating sheet of charge and is moving parallel to the sheet with speed 9.70 × 102 m/s. The sheet has uniform surface charge density 2.34 × 10-9 C/m2. What is the speed of the proton at
> In one experiment the electric field is measured for points at distances r from a uniform line of charge that has charge per unit length λ and length l, where l >> r. In a second experiment the electric field is measured for points at distances r from th
> (a). An insulating sphere with radius a has a uniform charge density
> A nonuniform, but spherically symmetric, distribution of charge has a charge density
> Repeat Problem 22.54, but now let the charge density of the slab be given by
> A slab of insulating material has thickness 2d and is oriented so that its faces are parallel to the yz-plane and given by the planes x = d and x = -d. The y- and z-dimensions of the slab are very large compared to d; treat them as essentially infinite.
> A nonuniform, but spherically symmetric, distribution of charge has a charge density r1r2 given as follows: where p(r) = po(1 - for r s R P(r) = 0 for r 2 R
> Because the charges on the electron and proton have the same absolute value, atoms are electrically neutral. Suppose that this is not precisely true, and the absolute value of the charge of the electron is less than the charge of the proton by 0.00100%.
> (a). How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere 30.0 cm in diameter to produce an electric field of magnitude 1390 N/C just outside the surface of the sphere? (b). What is the electric field a
> Using Thomson’s (outdated) model of the atom described in Problem 22.50, consider an atom consisting of two electrons, each of charge -e, embedded in a sphere of charge +2e and radius R. In equilibrium, each electron is a distance d fro
> Early in the 20th century, a leading model of the structure of the atom was that of English physicist J. J. Thomson (the discoverer of the electron). In Thomson’s model, an atom consisted of a sphere of positively charged material in wh
> An insulating hollow sphere has inner radius a and outer radius b. Within the insulating material the volume charge density is given by
> A solid conducting sphere with radius R carries a positive total charge Q. The sphere is surrounded by an insulating shell with inner radius R and outer radius 2R. The insulating shell has a uniform charge density
> Repeat Problem 22.45, but now let the outer shell have charge -2q. The inner shell still has charge +2q. Problem 22.45: A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell wit
> A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d (Fig. P22.45). The inner shell has total charge +2q, and the outer shell has charge +4
> A conducting spherical shell with inner radius a and outer radius b has a positive point charge Q located at its center. The total charge on the shell is -3Q, and it is insulated from its surroundings (Fig. P22.44). Fig. P22.44: (a). Derive expressio
> In a follow-up experiment, a charge of +40 pC was placed at the center of an artificial flower at the end of a 30-cmlong stem. Bees were observed to approach no closer than 15 cm from the center of this flower before they flew away. This observation sugg
> After one bee left a flower with a positive charge, that bee flew away and another bee with the same amount of positive charge flew close to the plant. Which diagram in Fig. P21.100 best represents the electric field lines between the bee and the flower?
> Two identical metal objects are mounted on insulating stands. Describe how you could place charges of opposite sign but exactly equal magnitude on the two objects.
> If you peel two strips of transparent tape off the same roll and immediately let them hang near each other, they will repel each other. If you then stick the sticky side of one to the shiny side of the other and rip them apart, they will attract each oth
> After a long day of driving you take a late-night swim in a motel swimming pool. When you go to your room, you realize that you have lost your room key in the pool. You borrow a powerful flashlight and walk around the pool, shining the light into it. The
> A series circuit has an impedance of 60.0 Ω and a power factor of 0.720 at 50.0 Hz. The source voltage lags the current. a. What circuit element, an inductor or a capacitor, should be placed in series with the circuit to raise its power factor? b. What
> A circular wire loop has a radius of 7.50 cm. A sinusoidal electromagnetic plane wave traveling in air passes through the loop, with the direction of the magnetic field of the wave perpendicular to the plane of the loop. The intensity of the wave at the
> A ray of light traveling in a block of glass (n = 1.52) is incident on the top surface at an angle of 57.2° with respect to the normal in the glass. If a layer of oil is placed on the top surface of the glass, the ray is totally reflected. What is the ma
> A source of sinusoidal electromagnetic waves radiates uniformly in all directions. At a distance of 10.0 m from this source, the amplitude of the electric field is measured to be 3.50 N/C. What is the electric-field amplitude 20.0 cm from the source?
> Two square reflectors, each 1.50 cm on a side and of mass 4.00 g, are located at opposite ends of a thin, extremely light, 1.00-m rod that can rotate without friction and in vacuum about an axle perpendicular to it through its center (Fig. P32.39). These
> When a solenoid is connected to a 48.0-V dc battery that has negligible internal resistance, the current in the solenoid is 5.50 A. When this solenoid is connected to an ac source that has voltage amplitude 48.0 V and angular frequency 20.0 rad/s, the cu
> A coworker of yours was making measurements of a large solenoid that is connected to an ac voltage source. Unfortunately, she left for vacation before she completed the analysis, and your boss has asked you to finish it. You are given a graph of 1/I2 ver
> A ray of light traveling in air is incident at angle θa on one face of a 90.0° prism made of glass. Part of the light refracts into the prism and strikes the opposite face at point A (Fig. P33.42). If the ray at A is at the critic
> A light ray in air strikes the right angle prism shown in Fig. P33.40. The prism angle at B is 30.0°. This ray consists of two different wavelengths. When it emerges at face AB, it has been split into two different rays that diverge from each
> The sun emits energy in the form of electromagnetic waves at a rate of 3.9 * 1026 W. This energy is produced by nuclear reactions deep in the sun’s interior. a. Find the intensity of electromagnetic radiation and the radiation pressure on an absorbing o
> A ray of light is incident in air on a block of a transparent solid whose index of refraction is n. If n = 1.38, what is the largest angle of incidence θa for which total internal reflection will occur at the vertical face (point A shown in
> A 400-Ω resistor and a 6.00-µF capacitor are connected in parallel to an ac generator that supplies an rms voltage of 180 V at an angular frequency of 360 rad/s. Use the results of Problem 31.54. Note that since there is no inductor in this circuit, the
> A horizontal cylindrical tank 2.20 m in diameter is half full of water. The space above the water is filled with a pressurized gas of unknown refractive index. A small laser can move along the curved bottom of the water and aims a light beam toward the c
> When the sun is either rising or setting and appears to be just on the horizon, it is in fact below the horizon. The explanation for this seeming paradox is that light from the sun bends slightly when entering the earth’s atmosphere, as shown in
> Figure P31.48 shows a low-pass filter (see Problem 31.47); the output voltage is taken across the capacitor in an L-R-C series circuit. Derive an expression for Vout /Vs, the ratio of the output and source voltage amplitudes, as a function of the angular
> A thin layer of ice (n = 1.309) floats on the surface of water (n = 1.333) in a bucket. A ray of light from the bottom of the bucket travels upward through the water. a. What is the largest angle with respect to the normal that the ray can make at the i
> A laser beam shines along the surface of a block of transparent material (see Fig. E33.8). Half of the beam goes straight to a detector, while the other half travels through the block and then hits the detector. The time delay between the arrival of the
> NASA is giving serious consideration to the concept of solar sailing. A solar sail craft uses a large, low mass sail and the energy and momentum of sunlight for propulsion. a. Should the sail be absorbing or reflective? Why? b. The total power output o
> The GPS network consists of 24 satellites, each of which makes two orbits around the earth per day. Each satellite transmits a 50.0-W (or even less) sinusoidal electromagnetic signal at two frequencies, one of which is 1575.42 MHz. Assume that a satellit
> a. Compute the reactance of a 0.450-H inductor at frequencies of 60.0 Hz and 600 Hz. b. Compute the reactance of a 2.50-µF capacitor at the same frequencies. c. At what frequency is the reactance of a 0.450-H inductor equal to that of a 2.50-µF capacit
> A light beam is directed parallel to the axis of a hollow cylindrical tube. When the tube contains only air, the light takes 8.72 ns to travel the length of the tube, but when the tube is filled with a transparent jelly, the light takes 1.82 ns longer to
> Very short pulses of high-intensity laser beams are used to repair detached portions of the retina of the eye. The brief pulses of energy absorbed by the retina weld the detached portions back into place. In one such procedure, a laser beam has a wavelen
> As a physics lab instructor, you conduct an experiment on standing waves of microwaves, similar to the standing waves produced in a microwave oven. A transmitter emits microwaves of frequency f. The waves are reflected by a flat metal reflector, and a re
> The company where you work has obtained and stored five lasers in a supply room. You have been asked to determine the intensity of the electromagnetic radiation produced by each laser. The lasers are marked with specifications, but unfortunately differen
> In a certain experiment, a radio transmitter emits sinusoidal electromagnetic waves of frequency 110.0 MHz in opposite directions inside a narrow cavity with reflectors at both ends, causing a standing-wave pattern to occur. a. How far apart are the nod
> A thin beam of white light is directed at a flat sheet of silicate flint glass at an angle of 20.0° to the surface of the sheet. Due to dispersion in the glass, the beam is spread out in a spectrum as shown in Fig. P33.56. The refractive index
> A beam of unpolarized sunlight strikes the vertical plastic wall of a water tank at an unknown angle. Some of the light reflects from the wall and enters the water (Fig. P33.55). The refractive index of the plastic wall is 1.61. If the light that has bee
> Light is incident in air at an angle θa (Fig. P33.54) on the upper surface of a transparent plate, the surfaces of the plate being plane and parallel to each other. a. Prove that θa = θ′ a. b. S
> The incident angle θa shown in Fig. P33.53 is chosen so that the light passes symmetrically through the prism, which has refractive index n and apex angle A. a. Show that the angle of deviation δ (the angle between the initial
> Light is incident normally on the short face of a 30°-60°-90° prism (Fig. P33.50). A drop of liquid is placed on the hypotenuse of the prism. If the index of refraction of the prism is 1.56, find the maximum index that th
> A parallel beam of light in air makes an angle of 47.5° with the surface of a glass plate having a refractive index of 1.66. a. What is the angle between the reflected part of the beam and the surface of the glass? b. What is the angle between the refr
> The prism shown in Fig. P33.49 has a refractive index of 1.66, and the angles A are 25.0°. Two light rays m and n are parallel as they enter the prism. What is the angle between them after they emerge? Figure P33.49 m A A n
> a. At what angular frequency is the voltage amplitude across the resistor in an L-R-C series circuit at maximum value? b. At what angular frequency is the voltage amplitude across the inductor at maximum value? c. At what angular frequency is the volta
> In an L-R-C series circuit the current is given by i = I cos ωt. The voltage amplitudes for the resistor, inductor, and capacitor are VR, VL, and VC. a. Show that the instantaneous power into the resistor is PR = VRIcos2ωt = 1/2VRI(1+cos2ωt). What does
> You are given this table of data recorded for a circuit that has a resistor, an inductor with negligible resistance, and a capacitor, all in series with an ac voltage source: Here f is the frequency of the voltage source, Z is the impedance of the circ
> You sight along the rim of a glass with vertical sides so that the top rim is lined up with the opposite edge of the bottom (Fig. P33.45a). The glass is a thin-walled, hollow cylinder 16.0 cm high. The diameter of the top and bottom of the glass is 8.0 c
> To vary the angle as well as the intensity of polarized light, ordinary unpolarized light is passed through one polarizer with its transmission axis vertical, and then a second polarizer is placed between the first polarizer and the insect. When the ligh
> Next, unpolarized light is reflected off a smooth horizontal piece of glass, and the reflected light shines on the insect. Which statement is true about the two types of cells? a. When the light is directly above the glass, only type V detects the refle
> First, light with a plane of polarization at 45° to the horizontal shines on the insect. Which statement is true about the two types of cells? a. Both types detect this light. b. Neither type detects this light. c. Only type H detects the light. d. O
> A secondary rainbow is formed when the incident light undergoes two internal reflections in a spherical drop of water as shown in Fig. 33.19e. (See Challenge Problem 33.60.) a. In terms of the incident angle θ a A and the refractive index n of the drop,
> In an L-R-C series ac circuit, the source has a voltage amplitude of 240 V, R = 90.0 Ω, and the reactance of the inductor is 320 Ω. The voltage amplitude across the resistor is 135 V. a. What is the current amplitude in the circuit? b. What is the volt
> Equation (31.9) says that vab = L di/dt (see Fig. 31.8a). Using Faraday’s law, explain why point a is at higher potential than point b when i is in the direction shown in Fig. 31.8a and is increasing in magnitude. When i is counterclock
> A beam of light traveling horizontally is made of an unpolarized component with intensity I0 and a polarized component with intensity Ip. The plane of polarization of the polarized component is oriented at an angle θ with respect to the vert
> Given small samples of three liquids, you are asked to determine their refractive indexes. However, you do not have enough of each liquid to measure the angle of refraction for light refracting from air into the liquid. Instead, for each liquid, you take
> In physics lab, you are studying the properties of four transparent liquids. You shine a ray of light (in air) onto the surface of each liquid—A, B, C, and D—one at a time, at a 60.0° angle of incidence; you
> The ICNIRP also has guidelines for magnetic-field exposure for the general public. In the frequency range of 25 Hz to 3 kHz, this guideline states that the maximum allowed magnetic field amplitude is 5/f T, where f is the frequency in kHz. Which is a mor
> The impedance of an L-R-C parallel circuit was derived in Problem 31.54. a. Show that at the resonance angular frequency v0 = 1/ LC , the impedance Z is a maximum and therefore the current through the ac source is a minimum. b. A 100-Ω resistor, a 0.10
> A resistor, an inductor, and a capacitor are connected in parallel to an ac source with voltage amplitude V and angular frequency ω. Let the source voltage be given by v = V cos ω t. a. Show that each of the instantaneous voltages vR, vL, and vC at any
> Electromagnetic waves propagate much differently in conductors than they do in dielectrics or in vacuum. If the resistivity of the conductor is sufficiently low (that is, if it is a sufficiently good conductor), the oscillating electric field of the wave
> The electron in a hydrogen atom can be considered to be in a circular orbit with a radius of 0.0529 nm and a kinetic energy of 13.6 eV. If the electron behaved classically, how much energy would it radiate per second (see Challenge Problem 32.51)? What d
> Electromagnetic radiation is emitted by accelerating charges. The rate at which energy is emitted from an accelerating charge that has charge q and acceleration a is given by where c is the speed of light. a. Verify that this equation is dimensionally
> An L-R-C series circuit is connected to an ac source of constant voltage amplitude V and variable angular frequency ω. Using the results of Problem 31.49, find an expression for a. the amplitude VL of the voltage across the inductor as a function of ω
> Medical x rays are taken with electromagnetic waves having a wavelength of around 0.10 nm in air. What are the frequency, period, and wave number of such waves?
> An L-R-C series circuit is connected to an ac source of constant voltage amplitude V and variable angular frequency ω. a. Show that the current amplitude, as a function of ω, is b. Show that the average power dissipated in the re
> An electromagnetic wave of wavelength 435 nm is traveling in vacuum in the –z-direction. The electric field has amplitude 2.70 * 10-3 V/m and is parallel to the x-axis. What are a. the frequency and b. the magnetic-field amplitude? c. Write the vector
> The microwaves in a certain microwave oven have a wavelength of 12.2 cm. a. How wide must this oven be so that it will contain five antinodal planes of the electric field along its width in the standing-wave pattern? b. What is the frequency of these m
> Scientists are working on a new technique to kill cancer cells by zapping them with ultrahigh-energy (in the range of 1012 W) pulses of light that last for an extremely short time (a few nanoseconds). These short pulses scramble the interior of a cell wi
> Three polarizing filters are stacked, with the polarizing axis of the second and third filters at 23.0° and 62.0°, respectively, to that of the first. If unpolarized light is incident on the stack, the light has intensity 55.0 W/cm2 after it passes throu
> A beam of polarized light passes through a polarizing filter. When the angle between the polarizing axis of the filter and the direction of polarization of the light is θ, the intensity of the emerging beam is I. If you now want the intensity to be I/2,
> A beam of unpolarized light of intensity I0 passes through a series of ideal polarizing filters with their polarizing axes turned to various angles as shown in Fig. E33.27. a. What is the light intensity (in terms of I0) at points A, B, and C? b. If w
> a. At what angle above the horizontal is the sun if sunlight reflected from the surface of a calm lake is completely polarized? b. What is the plane of the electric-field vector in the reflected light?
> Unpolarized light with intensity I0 is incident on two polarizing filters. The axis of the first filter makes an angle of 60.0° with the vertical, and the axis of the second filter is horizontal. What is the intensity of the light after it has passed thr
> A narrow beam of white light strikes one face of a slab of silicate flint glass. The light is traveling parallel to the two adjoining faces, as shown in Fig. E33.23. For the transmitted light inside the glass, through what angle ∆Î
