Two oppositely charged parallel plates produce a uniform electric field between them. An uncharged metal sphere is placed between the plates. Assume that the sphere is small enough that it does not affect the charge distribution on the plates. Sketch the electric field lines between the plates once electrostatic equilibrium is reached.
> A dc motor has coils with a resistance of 16 Ω and is connected to an emf of 120.0 V. When the motor operates at full speed, the back emf is 72 V. (a) What is the current in the motor when it first starts up? (b) What is the current when the motor is a
> Draw a circuit diagram for automobile headlights, connecting two separate bulbs and a switch to a single battery so that: (1) one switch turns both bulbs on and off and (2) one bulb still lights up even if the other bulb burns out.
> The wavelength of the fundamental standing wave on a cello string depends on which of these quantities: length of the string, mass per unit length of the string, or tension? The wavelength of the sound wave resulting from the string's vibration depends o
> Find the work done by gravity on the hanging crate.
> What are the advantages of using the concepts of stress and strain to describe deformations?
> A wheel of radius 30 cm is rotating at a rate of 2.0 revolutions every 0.080 s. (a) Through what angle, in radians, does the wheel rotate in 1.0 s? (b) What is the linear speed of a point on the wheel’s rim? (c) What is the wheel’s frequency of rotati
> As a Boeing 747 gains altitude, the passenger cabin is pressurized. However, the cabin is not pressurized fully to atmospheric (1.01 × 105 Pa), as it would be at sea level, but rather pressurized to 7.62 × 104 Pa. Suppose a 747 takes off from sea level w
> The lowest frequency string on a guitar is 65.5 cm long and is tuned to 82 Hz. (a) If the string has a mass of 3.31 g, what is the tension in the string? (b) By fingering the guitar at the fifth fret, you shorten the vibrating length of the string, the
> A 2 m long copper pipe is held vertically. When a marble is dropped down the pipe, it falls through in about 0.7 s. A magnet of similar size and shape dropped down the pipe takes much longer. Why?
> Think of a crystalline solid as a set of atoms connected by ideal springs. When a wire is stretched, how is the elongation of the wire related to the elongation of each of the interatomic springs? Use your answer to explain why a given tensile stress pro
> At a baseball game, a radar gun measures the speed of a 144 g baseball to be 137.32 ± 0.10 km/h. (a) What is the minimum uncertainty of the position of the baseball? (b) If the speed of a proton is measured to the same precision, what is the minimum unc
> Think of an example that illustrates why an “anti-Lenz” law would violate the conservation of energy. (The “anti-Lenz” law is: The direction of induced emfs and currents always reinforces the change that produces them.)
> Show that over one complete cycle, the average value of a sin2 ωt is . / Use the trigonometric identity sin2 ωt = (1 − cos 2ωt)/2.
> A car with a mass of 1700 kg is traveling directly northeast (45° between north and east) at a speed of 14 m/s (31 mi/h), and collides with a smaller car with a mass of 1300 kg that is traveling directly south at a speed of 18 m/s (40 mi/h). The two cars
> Vertically polarized light with intensity I0 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 (8), whe
> Given two identical, ideal batteries of emf / and two identical incandescent lightbulbs of resistance R (assumed constant), find the total power dissipated in the circuit in terms of / and R.
> The figure shows hysteresis curves for three different materials. A hysteresis curve is a plot of the magnetic field magnitude inside the material (B) as a function of the externally applied field (B0). (a) Which material would make the best permanent m
> A solenoid has 4850 turns per meter and radius 3.3 cm. The magnetic field inside has magnitude 0.24 T. What is the current in the solenoid?
> Two long, straight wires, each with a current of 5.0 A, are placed on two corners of an equilateral triangle with sides of length 3.2 cm as shown. One of the wires has a current into the page and one has a current out of the page. (a) What is the magnet
> You are designing the main solenoid for an MRI machine. The solenoid should be 1.5 m long. When the current is 80 A, the magnetic field inside should be 1.5 T. How many turns should your solenoid have?
> Two metal spheres have charges of equal magnitude, 3.2 × 10−14 C, but opposite sign. If the potential difference between the two spheres is 4.0 mV, what is the capacitance? [Hint: The “plates” are not parallel, but the definition of capacitance holds.]
> The strip in the diagram is used as a Hall probe to measure magnetic fields, (a) What happens if the strip is not perpendicular to the field? Does the Hall probe still read the correct field magnitude? Explain. (b) What happens if the field is in the p
> A 100 W incandescent lightbulb radiates visible light at a rate of about 10 W; the rest of the EM radiation is mostly infrared. Assume that the lightbulb radiates uniformly in all directions. Under ideal conditions, the eye can see the lightbulb if at le
> ɦ Photons of energy E = 4.000 keV undergo Compton scattering. What is the largest possible change in photon energy, measured as a fraction of the incident photon's energy (E − E′)/E?
> Two concentric circular wire loops in the same plane each carry a current. The larger loop has a current of 8.46 A circulating clockwise and has a radius of 6.20 cm. The smaller loop has a radius of 4.42 cm. What is the current in the smaller loop if the
> In naturally occurring potassium, 0.0117% of the nuclei are radioactive 40K. (a) What mass of 40K is found in a broccoli stalk containing 300 mg of potassium? (b) What is the activity of this broccoli stalk due to 40K?
> Two parallel wires in a horizontal plane carry currents I1 and I2 to the right. The wires each have length L and are separated by a distance d. Find the magnitudes and directions of the (a) the magnetic field due to wire 1 at the location of wire 2, (b
> Two long straight parallel wires separated by 8.0 cm carry currents of equal magnitude but heading in opposite directions. The wires are shown perpendicular to the plane of this page. Point P is 2.0 cm from wire 1, and the magnetic field at point P is 1.
> A dolphin wants to swim directly back to its home bay, which is 0.80 km due west. It can swim at a speed of 4.00 m/s relative to the water, but a uniform water current flows with speed 2.83 m/s in the southeast direction. (a) What direction should the d
> Speedometer readings are obtained and graphed as a car skids to a stop along a straight-line path. How far does the car move between t = 0 and t = 16 s? Sketch a motion diagram showing the position of the car at 2 s intervals and sketch a graph of x(t).
> A solenoid of length 0.256 m and radius 2.0 cm has 244 turns of wire. What is the magnitude of the magnetic field well inside the solenoid when there is a current of 4.5 A in the wire?
> Some animals are capable of detecting magnetic fields and use this sense to help them navigate. Suppose a high-voltage direct- current power line carries a current of 5.0 kA. (a) How far from the wire would a homing pigeon have to be so the field due to
> Which decay mode would you expect for radioactive /: α, β−, or β +? Explain. [Hint: Look at the neutron-to-proton ratio.]
> A standing wave has wavenumber 200 rad/m. What is the distance between two adjacent nodes?
> Unpolarized light is incident on a system of three ideal polarizers. The second polarizer is oriented at an angle of 30.0° with respect to the first, and the third is oriented at an angle of 45.0° with respect to the first. If the light that emerges from
> A point charge q = +3.0 nC moves through a potential difference ΔV = Vf − Vi = +25 V. What is the change in the electric potential energy?
> Within cells, small organelles containing newly synthesized proteins are transported along microtubules by tiny molecular motors called kinesins. What force does a kinesin molecule need to deliver in order to accelerate an organelle with mass 0.01 pg (10
> If the molecule is initially at rest at θ = 90.0°, what is its angular speed when it reaches θ = 0, assuming no other forces or torques? [Hint: First find the work done on each point charge.]
> Kieran measures the magnetic field of an electron beam. The beam strength is such that 1.40 × 1011 electrons pass a point every 1.30 μs. What magnetic field does Kieran measure at a distance of 2.00 cm from the beam center?
> Imagine a long straight wire perpendicular to the page and carrying a current I into the page. Sketch some field lines with arrowheads to indicate directions.
> The source and observer of a sound wave are both at rest with respect to the ground. The wind blows in the direction from source to observer. Is the observed frequency Doppler-shifted? Explain.
> Estimate the magnetic field at distances of 1 μm and 1 mm produced by a current of 3 μA along the medial nerve of the human arm. Model the nerve as a straight current-carrying wire. Compare with the magnitude of Earth's magnetic field near the surface, a
> An object of 1.0 kg mass approaches a stationary object of 5.0 kg at 10.0 m/s and, after colliding, rebounds in the reverse direction along the same line with a speed of 5.0 m/s. What is the speed of the 5.0 kg object after the collision?
> Explain how an automobile airbag protects the passenger from injury. Why would the airbag be ineffective if the gas pressure inside is too low when the passenger comes into contact with it? What about if it is too high?
> What is the momentum of an automobile (weight = 9800 N) when it is moving at 35 m/s to the south?
> Use the following method to show that the torque on an irregularly shaped planar loop due to a perpendicular magnetic field is Ï„ = NIAB. The irregular loop of current in part (a) of the figure carries current I. There is a perpendicular magne
> Deuterium (2D) is an isotope of hydrogen with a nucleus containing one proton and one neutron. In a 2D-2D fusion reaction, two deuterium nuclei combine to form a helium-3 nucleus plus a neutron, releasing energy in the process. The two 2D nuclei must ove
> Sketch some magnetic field lines for two identical bar magnets in the given configuration. Be sure to show field lines inside the magnets as well as outside.
> An aluminum rod, 1.0 m long, is held lightly in the middle. One end is struck head-on with a rubber mallet so that a longitudinal pulse—a sound wave—travels down the rod. The fundamental frequency of the longitudinal vibration is 2.55 kHz. (a) Describe
> A space rock contains 3.00 g of / and 0.150 g of /. / decays to / with a half-life of 1.06 × 1011 yr. If the rock originally contained no / , how old is it?
> In Chapter 19 we will see that a charged particle can undergo uniform circular motion when acted on by a magnetic force and no other forces. (a) For that to be true, what must be the angle between the magnetic force and the particle’s velocity? (b) The
> In this problem, you derive the expression for the self-inductance of a long solenoid [Eq. (20-30)]. The solenoid has n turns per unit length, length ℓ, and radius r. Assume that the current flowing in the solenoid is I. (a) Write an expression for the
> Parallel light of wavelength λ strikes a slit of width a at normal incidence. The light is viewed on a screen that is 1.0 m past the slits. In each case that follows, sketch the intensity on the screen as a function of x, the distance from the center of
> If gear A in Problem 73 has an initial frequency of 0.955 Hz and an angular acceleration of 3.0 rad/s2, how many rotations does each gear go through in 2.0 s?
> Sketch some magnetic field lines for two identical bar magnets in the given configuration. Be sure to show field lines inside the magnets as well as outside.
> A lid is put on a box that is 15 cm long, 13 cm wide, and 8.0 cm tall, and the box is then evacuated until its inner pressure is 0.80 × 105 Pa. How much force is required to lift the lid (a) at sea level; (b) in Denver, on a day when the atmospheric pr
> Sketch some magnetic field lines for two identical bar magnets in the given configuration. Be sure to show field lines inside the magnets as well as outside.
> A current I = 40.0 A flows through a strip of metal. An electromagnet is switched on so that there is a uniform magnetic field of magnitude 0.30 T directed into the page. How would you hook up a voltmeter to measure the Hall voltage? Show how the voltmet
> Crossed electric and magnetic fields are established over a certain region. The magnetic field is 0.635 T vertically downward. The electric field is 2.68 × 106 V/m horizontally east. An electron, traveling horizontally northward, experiences zero net for
> Show that the time for one revolution of a charged particle moving perpendicular to a uniform magnetic field is independent of its speed. (This is the principle on which the cyclotron operates.) In doing so, write an expression that gives the period T (t
> A sample containing sulfur (atomic mass 32 u), manganese (55 u), and an unknown element is analyzed in a mass spectrometer. As in Fig. 19.17(a), the ions move around half a circle before striking a photographic plate. The sulfur and manganese ions are se
> A 402 kg pile driver is raised 12 m above ground. (a) How much work must be done to raise the pile driver? (b) How much work does gravity do on the driver as it is raised? (c) The driver is now dropped. How much work does gravity do on the driver as i
> Peggy drives from Cornwall to Atkins Glen in 45 min. Cornwall is 73.6 km from Illium in a direction 25° west of south. Atkins Glen is 27.2 km from Illium in a direction 15° south of west. Using Illium as your origin, (a) draw the initial and final posit
> A battery charger delivers a current of 3.0 A for 4.0 h to a 12 V storage battery. What is the total charge that passes through the battery in that time?
> Radium-226 decays as /. If the / nucleus is at rest before the decay and the / nucleus is in its ground state, estimate the kinetic energy of the alpha particle. (Assume that the / nucleus takes away an insignificant fraction of the kinetic energy
> A boy of mass 60.0 kg is rescued from a hotel fire by leaping into a firefighters' net. The window from which he leapt was 8.0 m above the net. The firefighters lower their arms as he lands in the net so that he is brought to a complete stop in a time of
> A rectangular loop of wire, carrying current I1 = 2.0 mA, is next to a very long wire carrying a current I2 = 8.0 A. (a) What is the direction of the magnetic force on each of the four sides of the rectangle due to the long wire's magnetic field? (b) C
> A sample containing 12C, 16O, and an unknown isotope is analyzed in a mass spectrometer. As in Fig. 19.17(a), the ions move around a semicircle before striking a photographic plate. The 12C+ and 16O+ ions are separated by 2.250 cm on the plate, and the u
> After being accelerated through a potential difference of 5.0 kV, a singly charged 12C+ ion moves in a circle of radius 21 cm in the magnetic field of a mass spectrometer. What is the magnitude of the field?
> An electromagnetic flowmeter is used to measure blood flow rates during surgery. Blood containing Na+ ions flows due south through an artery with a diameter of 0.40 cm. The artery is in a downward magnetic field of 0.25 T and develops a Hall voltage of 0
> Naturally occurring carbon consists of two different isotopes (excluding 14C, which is present in only trace amounts). The most abundant isotope is 12C. When carbon is placed in a mass spectrometer, 12C+ ions moved in a circle of radius 15.0 cm, whereas
> In free fall, we assume the acceleration to be constant. Not only is air resistance ignored, but the gravitational field strength is assumed to be constant. From what height can an object fall to Earth's surface such that the gravitational field strength
> An alpha particle with a kinetic energy of 1.0 MeV is headed straight toward a gold nucleus. (a) Find the distance of closest approach between the centers of the alpha particle and gold nucleus. (Assume the gold nucleus remains stationary. Since its mas
> In one type of mass spectrometer, ions having the same velocity move through a uniform magnetic field. The spectrometer is being used to distinguish 12C+ and 14C+ ions. The 12C+ ions move in a circle of diameter 25 cm. (a) What is the diameter of the or
> Which of these unidentified nuclides are isotopes of each other?
> Calculate the mass density of nuclear matter.
> (a) Use Gauss’s law to prove that the electric field outside any spherically symmetrical charge distribution is the same as if all of the charge were concentrated into a point charge. (b) Now use Gauss’s law to prove that the electric field inside a sph
> Pascal’s principle: proof by contradiction. Points A and B are near each other at the same height in a fluid. Suppose PA > PB. (a) Can both vA and vB be zero? Explain. (b) Point C is just above point D in a static fluid. Suppose the pressure at C incre
> Sketch some magnetic field lines for two identical bar magnets in the given configuration. Be sure to show field lines inside the magnets as well as outside.
> A singly charged ion of unknown mass moves in a circle of radius 12.5 cm in a magnetic field of 1.2 T. The ion was accelerated through a potential difference of 7.0 kV before it entered the magnetic field. What is the mass of the ion?
> In a photoelectric experiment using sodium, when incident light of wavelength 570 nm and intensity 1.0 W/m2 is used, the measured stopping potential is 0.28 V. (a) What would the stopping potential be for incident light of wavelength 400.0 nm and intens
> Horizontally polarized light with intensity I0 passes through two ideal polarizers, one after the other. The transmission axes of the first and second polarizers are at angles θ1 and θ2, respectively, to the horizontal. Rank the intensities of the light
> A beam of α particles (helium nuclei) is used to treat a tumor located 10.0 cm inside a patient. To penetrate to the tumor, the α particles must be accelerated to a speed of 0.458c, where c is the speed of light. (Ignore relativistic effects.) The mass o
> Six protons move (at speed v) in magnetic fields (magnitude B) along circular paths. Rank them in order of the radius of their paths, greatest to smallest. (a) v = 6 × 106 m/s, B = 0.3 T (b) v = 3 × 106 m/s, B = 0.6 T (c) v = 3 × 106 m/s, B = 0.1 T (d)
> What is the electric force on the chloride ion in the lower right- hand corner in the diagram? Since the ions are in water, the “effective charge” on the chloride ions (Cl−) is −2 &A
> When two particles travel through a region of uniform magnetic field pointing out of the plane of the paper, they follow the trajectories shown. What are the signs of the charges of each particle?
> An electromagnetic flowmeter is used to measure blood flow rates during surgery. Blood containing ions (primarily Na+) flows through an artery with a diameter of 0.50 cm. The artery is in a magnetic field of 0.35 T and develops a Hall voltage of 0.60 mV
> A positron (q = +e) moves at 5.0 × 107 m/s in a magnetic field of magnitude 0.47 T. The magnetic force on the positron has magnitude 2.3 × 10−12 N. (a) What is the component of the positron's velocity perpendicular to the magnetic field? (b) What is th
> In a CRT, electrons moving at 1.8 × 107 m/s pass between the poles of an electromagnet where the magnetic field is 2.0 mT directed upward. (a) What is the radius of their circular path while in the magnetic field? (b) The time the electron
> If the pressure amplitude of a sound wave is doubled, what happens to the displacement amplitude, the intensity, and the intensity level?
> Find the electric potential energy for the following array of charges: charge q1 = +4.0 µC is located at (x, y) = (0.0, 0.0) m; charge q2 = +3.0 µC is located at (4.0, 3.0) m; and charge q3 = −1.0 µC is located at (0.0, 3.0) m.
> A certain electric device has the current-voltage (I-V) graph shown with Problem 30. What is the power dissipated at points 1 and 2?
> A cosmic ray muon with the same charge as an electron and a mass of 1.9 × 10−28 kg is moving toward the ground at an angle of 25° from the vertical with a speed of 7.0 × 107 m/s. As it crosses point
> A 100 g ball collides elastically with a 300 g ball that is at rest. If the 100 g ball was traveling in the positive x-direction at 5.00 m/s before the collision, what are the velocities of the two balls after the collision?
> A sample of gold, , decays radioactively with an initial rate of 1.00 × 1010 Bq into / . The half-life is 2.70 days. (a) What is the decay rate after 8.10 days? (b) What particle or particles are emitted during this decay process?
> Common sports injuries result in the tearing of tendons and ligaments due to overstretching. If the anterior cruciate ligament (ACL) in an athlete’s knee has a length of 1.0 cm, a breaking point of 190 MPa, and a Young’s modulus of 600 MPa, how far must
> (a) Show that the number of electron states in a sub-shell is 4â„“ + 2. [Hint: First, how many states are in each orbital? Second, how many orbitals are in each subshell?] (b) By summing the number of states in each of subshells, show th
> A variable inductor can be placed in series with a lightbulb to act as a dimmer. (a) What inductance would reduce the current through a 100 W lightbulb to 75% of its maximum value? Assume a 120 V rms, 60 Hz source. (b) Could a variable resistor be used
> The energy at which the fundamental forces are expected to unify is about 1019 GeV. Find the mass (in SI units) of a particle with rest energy 1019 GeV.
> At a certain point on Earth's surface in the southern hemisphere, the magnetic field has a magnitude of 5.0 × 10−5 T and points upward and toward the north at an angle of 55° above the horizontal. A cosmic ray muon with the same charge as an electron and
