The definition of resistivity (r = E/J) implies that an electric field exists inside a conductor. Yet we saw in Chapter 21 that there can be no electrostatic electric field inside a conductor. Is there a contradiction here? Explain.
> Pure silicon at room temperature contains approximately 1.0 × 1016 free electrons per cubic meter. (a). Referring to Table 25.1, calculate the mean free time t for silicon at room temperature. Table 25.1: (b). Your answer in part (a) is
> The battery for a certain cell phone is rated at 3.70 V. According to the manufacturer it can produce 3.15 × 104 J of electrical energy, enough for 5.25 h of operation, before needing to be recharged. Find the average current that this cell phone draws w
> Ordinary household electric lines in North America usually operate at 120 V. Why is this a desirable voltage, rather than a value considerably larger or smaller? On the other hand, automobiles usually have 12-V electrical systems. Why is this a desirable
> A battery-powered global positioning system (GPS) receiver operating on 9.0 V draws a current of 0.13 A. How much electrical energy does it consume during 30 minutes?
> When a resistor with resistance R is connected to a 1.50-V flashlight battery, the resistor consumes 0.0625 W of electrical power. (Throughout, assume that each battery has negligible internal resistance.) (a). What power does the resistor consume if it
> A carbon resistor is to be used as a thermometer. On a winter day when the temperature is 4.0°C, the resistance of the carbon resistor is 217.3 Ω. What is the temperature on a spring day when the resistance is 215.8 Ω? (Take the reference temperature T0
> You apply a potential difference of 4.50 V between the ends of a wire that is 2.50 m in length and 0.654 mm in radius. The resulting current through the wire is 17.6 A. What is the resistivity of the wire?
> What diameter must a copper wire have if its resistance is to be the same as that of an equal length of aluminum wire with diameter 2.14 mm?
> A parallel-plate capacitor has the volume between its plates filled with plastic with dielectric constant K. The magnitude of the charge on each plate is Q. Each plate has area A, and the distance between the plates is d. (a). Use Gauss’s law as stated
> In household wiring, copper wire 2.05 mm in diameter is often used. Find the resistance of a 24.0-m length of this wire.
> A ductile metal wire has resistance R. What will be the resistance of this wire in terms of R if it is stretched to three times its original length, assuming that the density and resistivity of the material do not change when the wire is stretched? (Hint
> Nerve cells transmit electric signals through their long tubular axons. These signals propagate due to a sudden rush of Na+ ions, each with charge +e, into the axon. Measurements have revealed that typically about 5.6 × 1011 Na+ ions enter each meter of
> A silver wire 2.6 mm in diameter transfers a charge of 420 C in 80 min. Silver contains 5.8 × 1028 free electrons per cubic meter. (a). What is the current in the wire? (b). What is the magnitude of the drift velocity of the electrons in the wire?
> Long-distance, electric-power, transmission lines always operate at very high voltage, sometimes as much as 750 kV. What are the advantages of such high voltages? What are the disadvantages?
> Certain sharks can detect an electric field as weak as 1.0 µV/m. To grasp how weak this field is, if you wanted to produce it between two parallel metal plates by connecting an ordinary 1.5-V AA battery across these plates, how far apart would the plates
> A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 12.5 cm, and the outer sphere has radius 14.8 cm. A potential difference of 120 V is applied to the capacitor. (a). What is the energy
> An air capacitor is made from two flat parallel plates 1.50 mm apart. The magnitude of charge on each plate is 0.0180 µC when the potential difference is 200 V. (a). What is the capacitance? (b). What is the area of each plate? (c). What maximum volta
> A 5.80-µF, parallel-plate, air capacitor has a plate separation of 5.00 mm and is charged to a potential difference of 400 V. Calculate the energy density in the region between the plates, in units of J/m3.
> A capacitor is made from two hollow, coaxial, iron cylinders, one inside the other. The inner cylinder is negatively charged and the outer is positively charged; the magnitude of the charge on each is 10.0 pC. The inner cylinder has radius 0.50 mm, the o
> A 5.00-pF, parallel-plate, air-filled capacitor with circular plates is to be used in a circuit in which it will be subjected to potentials of up to 1.00 × 102 V. The electric field between the plates is to be no greater than 1.00 × 104 N/C. As a budding
> A parallel-plate air capacitor is to store charge of magnitude 240.0 pC on each plate when the potential difference between the plates is 42.0 V. (a). If the area of each plate is 6.80 cm2, what is the separation between the plates? (b). If the separat
> Cathode-ray-tube oscilloscopes have parallel metal plates inside them to deflect the electron beam. These plates are called the deflecting plates. Typically, they are squares 3.0 cm on a side and separated by 5.0 mm, with vacuum in between. What is the c
> A parallel-plate air capacitor of capacitance 245 pF has a charge of magnitude 0.148 µC on each plate. The plates are 0.328 mm apart. (a). What is the potential difference between the plates? (b). What is the area of each plate? (c). What is the elect
> Which of the graphs in Fig. Q25.12 best illustrates the current I in a real resistor as a function of the potential difference V across it? Explain. Fig. Q25.12: (a) (b) (c) (d) V V
> The plates of a parallel-plate capacitor are 3.28 mm apart, and each has an area of 9.82 cm2. Each plate carries a charge of magnitude 4.35 × 10-8 C. The plates are in vacuum. What is (a). the capacitance; (b). the potential difference between the plate
> A spherical capacitor is formed from two concentric, spherical, conducting shells separated by vacuum. The inner sphere has radius 15.0 cm and the capacitance is 116 pF. (a). What is the radius of the outer sphere? (b). If the potential difference betw
> The plates of a parallel-plate capacitor are 2.50 mm apart, and each carries a charge of magnitude 80.0 nC. The plates are in vacuum. The electric field between the plates has a magnitude of 4.00 × 106 V/m. What is (a). the potential difference between
> A small particle has charge -5.00 µC and mass 2.00 × 10-4 kg. It moves from point A, where the electric potential is VA = +200 V, to point B, where the electric potential is VB = +800 V. The electric force is the only force acting on the particle. The pa
> The text states that good thermal conductors are also good electrical conductors. If so, why don’t the cords used to connect toasters, irons, and similar heat-producing appliances get hot by conduction of heat from the heating element?
> High-voltage power supplies are sometimes designed intentionally to have rather large internal resistance as a safety precaution. Why is such a power supply with a large internal resistance safer than a supply with the same voltage but lower internal res
> A fuse is a device designed to break a circuit, usually by melting when the current exceeds a certain value. What characteristics should the material of the fuse have?
> A positive charge q is fixed at the point x = 0, y = 0, and a negative charge -2q is fixed at the point x = a, y = 0. (a). Show the positions of the charges in a diagram. (b). Derive an expression for the potential V at points on the x-axis as a functio
> Small aircraft often have 24-V electrical systems rather than the 12-V systems in automobiles, even though the electrical power requirements are roughly the same in both applications. The explanation given by aircraft designers is that a 24-V system weig
> Liquid dielectrics that have polar molecules (such as water) always have dielectric constants that decrease with increasing temperature. Why?
> The two plates of a capacitor are given charges ±Q. The capacitor is then disconnected from the charging device so that the charges on the plates can’t change, and the capacitor is immersed in a tank of oil. Does the electric field between the plates inc
> Eight flashlight batteries in series have an emf of about 12 V, similar to that of a car battery. Could they be used to start a car with a dead battery? Why or why not?
> The energy that can be extracted from a storage battery is always less than the energy that goes into it while it is being charged. Why?
> Electrolytic capacitors use as their dielectric an extremely thin layer of nonconducting oxide between a metal plate and a conducting solution. Discuss the advantage of such a capacitor over one constructed using a solid dielectric between the metal plat
> The freshness of fish can be measured by placing a fish between the plates of a capacitor and measuring the capacitance. How does this work? (Hint: As time passes, the fish dries out. See Table 24.1.) Table 24.1: Material K Material K Polyvinyl chl
> A light bulb glows because it has resistance. The brightness of a light bulb increases with the electrical power dissipated in the bulb. Fig. Q25.14: (a). In the circuit shown in Fig. Q25.14a, the two bulbs A and B are identical. Compared to bulb A,
> Why does an electric light bulb nearly always burn out just as you turn on the light, almost never while the light is shining?
> A rule of thumb used to determine the internal resistance of a source is that it is the open-circuit voltage divided by the short-circuit current. Is this correct? Why or why not?
> As shown in Table 24.1, water has a very large dielectric constant K = 80.4. Why do you think water is not commonly used as a dielectric in capacitors? Table 24.1: Material K Material K Polyvinyl chloride Plexiglas® Vacuum 1 3.18 Air (1 atm) 1.0005
> A cylindrical rod has resistivity r. If we triple its length and diameter, what is its resistivity, in terms of r?
> We have seen that a coulomb is an enormous amount of charge; it is virtually impossible to place a charge of 1 C on an object. Yet, a current of 10 A, 10 C/s, is quite reasonable. Explain this apparent discrepancy.
> A conductor is an extreme case of a dielectric, since if an electric field is applied to a conductor, charges are free to move within the conductor to set up “induced charges.” What is the dielectric constant of a perfect conductor? Is it K = 0, K → q, o
> Suppose several different parallel-plate capacitors are charged up by a constant-voltage source. Thinking of the actual movement and position of the charges on an atomic level, why does it make sense that the capacitances are proportional to the surface
> Batteries are always labeled with their emf; for instance, an AA flashlight battery is labeled “1.5 volts.” Would it also be appropriate to put a label on batteries stating how much current they provide? Why or why not?
> A parallel-plate capacitor is charged by being connected to a battery and is then disconnected from the battery. The separation between the plates is then doubled. How does the electric field change? The potential difference? The total energy? Explain.
> A positive point charge q1 = +5.00 × 10-4 C is held at a fixed position. A small object with mass 4.00 × 10-3 kg and charge q2 = -3.00 × 10-4 C is projected directly at q1. Ignore gravity. When q2 is 0.400 m away, its speed is 800 m/s. What is its speed
> A point charge q1 = 4.00 nC is placed at the origin, and a second point charge q2 = -3.00 nC is placed on the x-axis at x = +20.0 cm. A third point charge q3 = 2.00 nC is to be placed on the x-axis between q1 and q2. (Take as zero the potential energy of
> A point charge q1 = +5.00 µC is held fixed in space. From a horizontal distance of 6.00 cm, a small sphere with mass 4.00 × 10-3 kg and charge q2 = +2.00 µC is fired toward the fixed charge with an initial speed of 40.0 m/s. Gravity can be neglected. Wha
> Electronic flash units for cameras contain a capacitor for storing the energy used to produce the flash. In one such unit, the flash lasts for 1 175 s with an average light power output of 2.70 × 105 W. (a). If the conversion of electrical energy to l
> What is the minimum amount of work that must be done by the cell to restore Vm to -70 mV? (a). 3 mJ; (b). 3 mJ; (c). 3 nJ; (d). 3 pJ.
> Suppose that the change in Vm was caused by the entry of Ca2+ instead of Na+. How many Ca2+ ions would have to enter the cell per unit membrane to produce the change? (a). Half as many as for Na+; (b). the same as for Na+; (c). twice as many as for Na
> Suppose that the egg has a diameter of 200 mm. What fractional change in the internal Na+ concentration results from the fertilization-induced change in Vm? Assume that Na+ ions are distributed throughout the cell volume. The concentration increases by
> Electrons in an electric circuit pass through a resistor. The wire on either side of the resistor has the same diameter. (a). How does the drift speed of the electrons before entering the resistor compare to the speed after leaving the resistor? Explain
> How many moles of Na+ must m ove per unit area of membrane to change Vm from -70 mV to +30 mV, if we assume that the membrane behaves purely as a capacitor? (a). 10-4 mol/cm2; (b). 10-9 mol/cm2; (c). 10-12 mol/cm2; (d). 10-14 mol/cm2.
> Two square conducting plates with sides of length L are separated by a distance D. A dielectric slab with constant K with dimensions L × L × D is inserted a distance x into the space between the plates, as shown in Fig. P24.72.
> You are designing capacitors for various applications. For one application, you want the maximum possible stored energy. For another, you want the maximum stored charge. For a third application, you want the capacitor to withstand a large applied voltage
> Your electronics company has several identical capacitors with capacitance C1 and several others with capacitance C2. You must determine the values of C1 and C2 but don’t have access to C1 and C2 individually. Instead, you have a network with C1 and C2 c
> A parallel-plate capacitor is made from two plates 12.0 cm on each side and 4.50 mm apart. Half of the space between these plates contains only air, but the other half is filled with Plexiglas® of dielectric constant 3.40 (Fig. P24.66). An 18.
> A potential difference Vab = 48.0 V is applied across the capacitor network of Fig. E24.17. If C1 = C2 = 4.00 mF and C4 = 8.00 mF, what must the capacitance C3 be if the network is to store 2.90 × 10-3 J of electrical energy? Fig. E24.17:
> A parallel-plate capacitor with only air between the plates is charged by connecting it to a battery. The capacitor is then disconnected from the battery, without any of the charge leaving the plates. (a). A voltmeter reads 45.0 V when placed across the
> Each combination of capacitors between points a and b in Fig. P24.60 is first connected across a 120-V battery, charging the combination to 120 V. These combinations are then connected to make the circuits shown. When the switch S is thrown, a surge of c
> In Fig. P24.59, each capacitance C1 is 6.9 µF, and each capacitance C2 is 4.6 µF. Fig. P24.59: (a). Compute the equivalent capacitance of the network between points a and b. (b). Compute the charge on each of the three capac
> Three capacitors having capacitances of 8.4, 8.4, and 4.2 µF are connected in series across a 36-V potential difference. (a). What is the charge on the 4.2-µF capacitor? (b). What is the total energy stored in all three capacitors? (c). The capacitors
> A parallel-plate capacitor is connected to a power supply that maintains a fixed potential difference between the plates. (a). If a sheet of dielectric is then slid between the plates, what happens to (i). the electric field between the plates, (ii). t
> The capacitors in Fig. P24.56 are initially uncharged and are connected, as in the diagram, with switch S open. The applied potential difference is Vab = +210 V. Fig. P24.56: (a). What is the potential difference Vcd? (b). What is the potential diff
> In Fig. E24.20, C1 = 3.00 µF and Vab = 150 V. The charge on capacitor C1 is 150 µC and the charge on C3 is 450 µC. What are the values of the capacitances of C2 and C3? Fig. E24.20: (a) No dielectric (b) Diele
> Current materials-science technology allows engineers to construct capacitors with much higher values of C than were previously possible. A capacitor has C = 3000 F and is rated to withstand a maximum potential difference of 2.7 V. The cylindrical capaci
> In Fig. P24.53, C1 = C5 = 8.4 µF and C2 = C3 = C4 = 4.2 µF. The applied potential is Vab = 220 V. Fig. P24.53: (a). What is the equivalent capacitance of the network between points a and b? (b). Calculate the charge on each
> In Fig. E24.17, C1 = 6.00 mF, C2 = 3.00 mF, C3 = 4.00 µF, and C4 = 8.00 µF. The capacitor network is connected to an applied potential difference Vab. After the charges on the capacitors have reached their final values, the volt
> For the capacitor network shown in Fig. P24.51, the potential difference across ab is 12.0 V. Find Fig. P24.51: (a). the total energy stored in this network and (b). the energy stored in the 4.80-µF capacitor. 6.20 μF 11.8 μF 8.60 μ
> In Fig. 24.9a, let C1 = 9.0 µF, C2 = 4.0 µF, and Vab = 64 V. Suppose the charged capacitors are disconnected from the source and from each other, and then reconnected to each other with plates of opposite sign together. By how m
> A 20.0-µF capacitor is charged to a potential difference of 800 V. The terminals of the charged capacitor are then connected to those of an uncharged 10.0-µF capacitor. Compute (a). the original charge of the system, (b). the final potential difference
> Cell membranes (the walled enclosure around a cell) are typically about 7.5 nm thick. They are partially permeable to allow charged material to pass in and out, as needed. Equal but opposite charge densities build up on the inside and outside faces of su
> A helium ion (He++) that comes within about 10 fm of the center of the nucleus of an atom in the sample may induce a nuclear reaction instead of simply scattering. Imagine a helium ion with a kinetic energy of 3.0 MeV heading straight toward an atom at r
> In terms of the dielectric constant K, what happens to the electric flux through the Gaussian surface shown in Fig. 24.22 when the dielectric is inserted into the previously empty space between the plates? Explain. Fig. 24.22: E = 0 Conductor Diele
> For a particular experiment, helium ions are to be given a kinetic energy of 3.0 MeV. What should the voltage at the center of the accelerator be, assuming that the ions start essentially at rest? (a). -3.0 MV; (b). +3.0 MV; (c). +1.5 MV; (d). +1.0 M
> In experiments in which atomic nuclei collide, head-on collisions like that described in Problem 23.74 do happen, but “near misses” are more common. Suppose the alpha particle in that problem is not “aimed” at the center of the lead nucleus but has an in
> A hollow, thin-walled insulating cylinder of radius R and length L (like the cardboard tube in a roll of toilet paper) has charge Q uniformly distributed over its surface. (a). Calculate the electric potential at all points along the axis of the tube. T
> The charge of an electron was first measured by the American physicist Robert Millikan during 1909–1913. In his experiment, oil was sprayed in very fine drops (about 10-4 mm in diameter) into the space between two parallel horizontal pl
> A small, stationary sphere carries a net charge Q. You perform the following experiment to measure Q: From a large distance you fire a small particle with mass m = 4.00 × 10-4 kg and charge q = 5.00 × 10-8 C directly at the cent
> The electric potential in a region that is within 2.00 m of the origin of a rectangular coordinate system is given by V = Axl + Bym + Czn + D, where A, B, C, D, l, m, and n are constants. The units of A, B, C, and D are such that if x, y, and z are in me
> In one type of computer keyboard, each key holds a small metal plate that serves as one plate of a parallel-plate, air filled capacitor. When the key is depressed, the plate separation decreases and the capacitance increases. Electronic circuitry detects
> The source of the sun’s energy is a sequence of nuclear reactions that occur in its core. The first of these reactions involves the collision of two protons, which fuse together to form a heavier nucleus and release energy. For this pro
> A metal sphere with radius R1 has a charge Q1. Take the electric potential to be zero at an infinite distance from the sphere. (a). What are the electric field and electric potential at the surface of the sphere? This sphere is now connected by a long, t
> Will a light bulb glow more brightly when it is connected to a battery as shown in Fig. Q25.16a, in which an ideal ammeter A is placed in the circuit, or when it is connected as shown in Fig. 25.16b, in which an ideal voltmeter V is placed in the circuit
> An alpha particle with kinetic energy 9.50 MeV (when far away) collides head-on with a lead nucleus at rest. What is the distance of closest approach of the two particles? (Assume that the lead nucleus remains stationary and may be treated as a point cha
> Electric charge is distributed uniformly along a thin rod of length a, with total charge Q. Take the potential to be zero at infinity. Find the potential at the following points (Fig. P23.73): Fig. P23.73): (a) point P, a distance x to the right of th
> a). If a spherical raindrop of radius 0.650 mm carries a charge of -3.60 pC uniformly distributed over its volume, what is the potential at its surface? (Take the potential to be zero at an infinite distance from the raindrop.) (b). Two identical raindr
> You are conducting experiments with an air filled parallel-plate capacitor. You connect the capacitor to a battery with voltage 24.0 V. Initially the separation d between the plates is 0.0500 cm. In one experiment, you leave the battery connected to the
> An insulating spherical shell with inner radius 25.0 cm and outer radius 60.0 cm carries a charge of +150.0 µC uniformly distributed over its outer surface. Point a is at the center of the shell, point b is on the inner surface, and point c is on the out
> Charge Q = +4.00 µC is distributed uniformly over the volume of an insulating sphere that has radius R = 5.00 cm. What is the potential difference between the center of the sphere and the surface of the sphere?
> A fuel gauge uses a capacitor to determine the height of the fuel in a tank. The effective dielectric constant Keff changes from a value of 1 when the tank is empty to a value of K, the dielectric constant of the fuel, when the tank is full. The appropri
> A solid sphere of radius R contains a total charge Q distributed uniformly throughout its volume. Find the energy needed to assemble this charge by bringing infinitesimal charges from far away. This energy is called the “self-energy” of the charge distri
> A disk with radius R has uniform surface charge density
> Electrostatic precipitators use electric forces to remove pollutant particles from smoke, in particular in the smokestacks of coal-burning power plants. One form of precipitator consists of a vertical, hollow, metal cylinder with a thin wire, insulated f
> An ideal ammeter A is placed in a circuit with a battery and a light bulb as shown in Fig. Q25.15a, and the ammeter reading is noted. The circuit is then reconnected as in Fig. Q25.15b, so that the positions of the ammeter and light bulb are reversed.
