Two spherical shells have a common center. The inner shell has radius R1 = 5.00 cm and charge q1 = +3.00 × 10-6 C; the outer shell has radius R2 = 15.0 cm and charge q2 = -5.00 × 10-6 C. Both charges are spread uniformly over the shell surface. What is the electric potential due to the two shells at the following distances from their common center: (a). r = 2.50 cm; (b). r = 10.0 cm; (c). r = 20.0 cm? Take V = 0 at a large distance from the shells.
> 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.
> The vertical deflecting plates of a typical classroom oscilloscope are a pair of parallel square metal plates carrying equal but opposite charges. Typical dimensions are about 3.0 cm on a side, with a separation of about 5.0 mm. The potential difference
> Cathode-ray tubes (CRTs) were often found in oscilloscopes and computer monitors. In Fig. P23.63 an electron with an initial speed of 6.50 × 106 m/s is projected along the axis midway between the deflection plates of a cathode-ray tube. The
> An air capacitor is made by using two flat plates, each with area A, separated by a distance d. Then a metal slab having thickness a (less than d) and the same shape and size as the plates is inserted between them, parallel to the plates and not touching
> A long metal cylinder with radius a is supported on an insulating stand on the axis of a long, hollow, metal tube with radius b. The positive charge per unit length on the inner cylinder is l, and there is an equal negative charge per unit length on the
> A small sphere with mass 1.50 g hangs by a thread between two very large parallel vertical plates 5.00 cm apart (Fig. P23.59). The plates are insulating and have uniform surface charge densities +
> A parallel-plate air capacitor is made by using two plates 12 cm square, spaced 3.7 mm apart. It is connected to a 12-V battery. (a). What is the capacitance? (b). What is the charge on each plate? (c). What is the electric field between the plates? (
> Figure P23.57 shows eight point charges arranged at the corners of a cube with sides of length d. The values of the charges are +q and -q, as shown. This is a model of one cell of a cubic ionic crystal. In sodium chloride (NaCl), for instance, the positi
> Two oppositely charged, identical insulating spheres, each 50.0 cm in diameter and carrying a uniformly distributed charge of magnitude 250 µC, are placed 1.00 m apart center to center (Fig. P23.56). Fig. P23.56: (a). If a voltmeter is c
> A vacuum tube diode consists of concentric cylindrical electrodes, the negative cathode and the positive anode. Because of the accumulation of charge near the cathode, the electric potential between the electrodes is given by V(x) = Cx4/3 where x is th
> Suppose you bring a slab of dielectric close to the gap between the plates of a charged capacitor, preparing to slide it between the plates. What force will you feel? What does this force tell you about the energy stored between the plates once the diele
> Identical charges q = +5.00 µC are placed at opposite corners of a square that has sides of length 8.00 cm. Point A is at one of the empty corners, and point B is at the center of the square. A charge q0 = -3.00 µC is placed at point A and moves along th
> A particle with charge +7.60 nC is in a uniform electric field directed to the left. Another force, in addition to the electric force, acts on the particle so that when it is released from rest, it moves to the right. After it has moved 8.00 cm, the addi
> A proton and an alpha particle are released from rest when they are 0.225 nm apart. The alpha particle (a helium nucleus) has essentially four times the mass and two times the charge of a proton. Find the maximum speed and maximum acceleration of each of
> When radium-226 decays radioactively, it emits an alpha particle (the nucleus of helium), and the end product is radon-222. We can model this decay by thinking of the radium-226 as consisting of an alpha particle emitted from the surface of the spherical
> A small sphere with mass 5.00 × 10-7 kg and charge +7.00 µC is released from rest a distance of 0.400 m above a large horizontal insulating sheet of charge that has uniform surface charge density
> A gold nucleus has a radius of 7.3 × 10-15 m and a charge of +79e. Through what voltage must an alpha particle, with charge +2e, be accelerated so that it has just enough energy to reach a distance of 2.0 × 10-14 m from the surface of a gold nucleus? (As
> The power rating of a light bulb (such as a 100-W bulb) is the power it dissipates when connected across a 120-V potential difference. What is the resistance of? (a). a 100-W bulb and (b). a 60-W bulb? (c). How much current does each bulb draw in norm
> A “540-W” electric heater is designed to operate from 120-V lines. (a). What is its operating resistance? (b). What current does it draw? (c). If the line voltage drops to 110 V, what power does the heater take? (Assume that the resistance is constant
> In the circuit in Fig. E25.47, find Fig. E25.47: (a). the rate of conversion of internal (chemical) energy to electrical energy within the battery; (b). the rate of dissipation of electrical energy in the battery; (c). the rate of dissipation of elec
> A typical small flashlight contains two batteries, each having an emf of 1.5 V, connected in series with a bulb having resistance 17 Ω. (a). If the internal resistance of the batteries is negligible, what power is delivered to the bulb? (b). If the bat
> A capacitor made of aluminum foil strips separated by Mylar film was subjected to excessive voltage, and the resulting dielectric breakdown melted holes in the Mylar. After this, the capacitance was found to be about the same as before, but the breakdown
> A 25.0-Ω bulb is connected across the terminals of a 12.0-V battery having 3.50 Ω of internal resistance. What percentage of the power of the battery is dissipated across the internal resistance and hence is not available to the bulb?
> An idealized voltmeter is connected across the terminals of a 15.0-V battery, and a 75.0-Ω appliance is also connected across its terminals. If the voltmeter reads 11.9 V, (a). how much power is being dissipated by the appliance, and (b). what is the i
> The capacity of a storage battery, such as those used in automobile electrical systems, is rated in ampere-hours (A ∙ h). A 50-A ∙ h battery can supply a current of 50 A for 1.0 h, or 25 A for 2.0 h, and so on. (a). What total energy can be supplied by
> A heart defibrillator is used to enable the heart to start beating if it has stopped. This is done by passing a large current of 12 A through the body at 25 V for a very short time, usually about 3.0 ms. (a). What power does the defibrillator deliver to
> Electric eels generate electric pulses along their skin that can be used to stun an enemy when they come into contact with it. Tests have shown that these pulses can be up to 500 V and produce currents of 80 mA (or even larger). A typical pulse lasts for
> Consider the circuit of Fig. E25.30. Fig. E25.30: (a). What is the total rate at which electrical energy is dissipated in the 5.0- Ω and 9.0-Ω resistors? (b). What is the power output of the 16.0-V battery? (c). At what rate
> In Europe the standard voltage in homes is 220 V instead of the 120 V used in the United States. Therefore a “100-W” European bulb would be intended for use with a 220-V potential difference (see Problem 25.36). Problem 25.36: If a “75-W” bulb (see Pr
> If a “75-W” bulb (see Problem 25.35) is connected across a 220-V potential difference (as is used in Europe), how much power does it dissipate? Ignore the temperature dependence of the bulb’s resistance. Problem 25.35: The power rating of a light bulb
> Consider the circuit shown in Fig. E25.26. The terminal voltage of the 24.0-V battery is 21.2 V. What are Fig. E25.26: (a). the internal resistance r of the battery and (b) the resistance R of the circuit resistor? r 24.0 V ww 4.00 A R 4.00 A ww
> A copper transmission cable 100 km long and 10.0 cm in diameter carries a current of 125 A. (a). What is the potential drop across the cable? (b). How much electrical energy is dissipated as thermal energy every hour?
> Is dielectric strength the same thing as dielectric constant? Explain any differences between the two quantities. Is there a simple relationship between dielectric strength and dielectric constant (see Table 24.2)? Table 24.2: Dielectric Strength,
> The circuit shown in Fig. E25.33 contains two batteries, each with an emf and an internal resistance, and two resistors. Find Fig. E25.33: (a) the current in the circuit (magnitude and direction) and (b) the terminal voltage Vab of the 16.0-V batter
> In the circuit of Fig. E25.30, the 5.0-Ω resistor is removed and replaced by a resistor of unknown resistance R. When this is done, an ideal voltmeter connected across the points b and c reads 1.9 V. Find Fig. E25.30: (a). the current in
> In the circuit shown in Fig. E25.30, the 16.0-V battery is removed and reinserted with the opposite polarity, so that its negative terminal is now next to point a. Find Fig. E25.30: (a). the current in the circuit (magnitude and direction); (b). the
> The circuit shown in Fig. E25.30 contains two batteries, each with an emf and an internal resistance, and two resistors. Find Fig. E25.30: (a). the current in the circuit (magnitude and direction); (b). the terminal voltage Vab of the 16.0-V battery;
> When switch S in Fig. E25.29 is open, the voltmeter V reads 3.08 V. When the switch is closed, the voltmeter reading drops to 2.97 V, and the ammeter A reads 1.65 A. Find the emf, the internal resistance of the battery, and the circuit resistance R. Assu
> An idealized ammeter is connected to a battery as shown in Fig. E25.28. Find Fig. E25.28: (a). the reading of the ammeter, (b). the current through the 4.00-Ω resistor, (c). the terminal voltage of the battery. (A 2.00 Ω 10.0 V 4.00
> An ideal voltmeter V is connected to a 2.0-Ω resistor and a battery with emf 5.0 V and internal resistance 0.5 Ω as shown in Fig. E25.27. Fig. E25.27: (a). What is the current in the 2.0- Ω resistor? (b). What is t
> A 1.50-m cylindrical rod of diameter 0.500 cm is connected to a power supply that maintains a constant potential difference of 15.0 V across its ends, while an ammeter measures the current through it. You observe that at room temperature (20.0°C) the amm
> At room temperature, what is the strength of the electric field in a 12-gauge copper wire (diameter 2.05 mm) that is needed to cause a 4.50-A current to flow? (b). What field would be needed if the wire were made of silver instead?
> (a). What is the resistance of a Nichrome wire at 0.0°C if its resistance is 100.00 Ω at 11.5°C? (b). What is the resistance of a carbon rod at 25.8°C if its resistance is 0.0160 Ω at 0.0°C?
> Temperature coefficients of resistivity are given in Table 25.2. Table 25.2: (a). If a copper heating element is connected to a source of constant voltage, does the electrical power consumed by the heating element increase or decrease as its temperat
> A hollow aluminum cylinder is 2.50 m long and has an inner radius of 2.75 cm and an outer radius of 4.60 cm. Treat each surface (inner, outer, and the two end faces) as an equipotential surface. At room temperature, what will an ohmmeter read if it is co
> A current-carrying gold wire has diameter 0.84 mm. The electric field in the wire is 0.49 V/m. What are (a). the current carried by the wire; (b). the potential difference between two points in the wire 6.4 m apart; (c). the resistance of a 6.4-m leng
> A strand of wire has resistance 5.60 µΩ. Find the net resistance of 120 such strands if they are (a). placed side by side to form a cable of the same length as a single strand, and (b). connected end to end to form a wire 120 times as long as a single s
> A cylindrical tungsten filament 15.0 cm long with a diameter of 1.00 mm is to be used in a machine for which the temperature will range from room temperature (20°C) up to 120°C. It will carry a current of 12.5 A at all temperatures
> A wire 6.50 m long with diameter of 2.05 mm has a resistance of 0.0290 Ω. What material is the wire most likely made of?
> A 14-gauge copper wire of diameter 1.628 mm carries a current of 12.5 mA. (a). What is the potential difference across a 2.00-m length of the wire? (b). What would the potential difference in part (a) be if the wire were silver instead of copper, but a
> A copper wire has a square cross section 2.3 mm on a side. The wire is 4.0 m long and carries a current of 3.6 A. The density of free electrons is 8.5 × 1028/m3. Find the magnitudes of (a). the current density in the wire and (b). the electric field in
> During lightning strikes from a cloud to the ground, currents as high as 25,000 A can occur and last for about 40 µs. How much charge is transferred from the cloud to the earth during such a strike?
> Current passes through a solution of sodium chloride. In 1.00 s, 2.68 × 1016 Na+ ions arrive at the negative electrode and 3.92 × 1016 Cl- ions arrive at the positive electrode. (a). What is the current passing between the electrodes? (b). What is the
> The current in a wire varies with time according to the relationship I = 55 A – (0.65 A/s2) t2. (a). How many coulombs of charge pass a cross section of the wire in the time interval between t = 0 and t = 8.0 s? (b). What constant current would transpo
> You have two capacitors and want to connect them across a voltage source (battery) to store the maximum amount of energy. Should they be connected in series or in parallel?
> A point charge q1 = +2.40 µC is held stationary at the origin. A second point charge q2 = -4.30 µC moves from the point x = 0.150 m, y = 0 to the point x = 0.250 m, y = 0.250 m. How much work is done by the electric force on q2?
