Question: In the circuit shown in Fig. P29.

> Cell membranes across a wide variety of organisms have a capacitance per unit area of 1 µF/cm2. For the electrical signal in a nerve to propagate down the axon, the charge on the membrane “capacitor” must change. What time constant is required when the i

> In a simple model of an axon conducting a nerve signal, ions move across the cell membrane through open ion channels, which act as purely resistive elements. If a typical current density (current per unit cross-sectional area) in the cell membrane is 5 m

> Assume that a typical open ion channel spanning an axon’s membrane has a resistance of 1 × 1011 Ω . We can model this ion channel, with its pore, as a 12-nm-long cylinder of radius 0.3 nm. What is the resistivity of the fluid in the pore? (a). 10  Ω ∙

> The infinite network of resistors shown in Fig. P26.83 is known as an attenuator chain, since this chain of resistors causes the potential difference between the upper and lower wires to decrease, or attenuate, along the length of the chain. Fig. P26.8

> Suppose a resistor R lies along each edge of a cube (12 resistors in all) with connections at the corners. Find the equivalent resistance between two diagonally opposite corners of the cube (points a and b in Fig. P26.84). Fig. P26.84: b a

> As shown in Fig. P26.83, a network of resistors of resistances R1 and R2 extends to infinity toward the right. Prove that the total resistance RT of the infinite network is equal to (Hint: Since the network is infinite, the resistance of the network to

> In another experiment, a piece of the web is suspended so that it can move freely. When either a positively charged object or a negatively charged object is brought near the web, the thread is observed to move toward the charged object. What is the best

> A coil with magnetic moment 1.45 A ∙ m2 is oriented initially with its magnetic moment antiparallel to a uniform 0.835-T magnetic field. What is the change in potential energy of the coil when it is rotated 1800 so that its magnetic moment is parallel to

> The magnetic susceptibility of paramagnetic materials is quite strongly temperature dependent, but that of diamagnetic materials is nearly independent of temperature. Why the difference?

> What is the maximum current that flows in the thread during this experiment if the voltage source is a 9-V battery? (a). about 1 A; (b). about 0.1 A; (c). about 1 µA; (d). about 1 nA.

> If the conductivity of the thread results from the aqueous coating only, how does the cross-sectional area A of the coating compare when the thread is 13 mm long versus the starting length of 5 mm? Assume that the resistivity of the coating remains const

> What is the best explanation for the behavior exhibited in the data? (a). Longer threads can carry more current than shorter threads do and so make better electrical conductors. (b). The thread stops being a conductor when it is stretched to 13 mm, due

> An external resistor with resistance R is connected to a battery that has emf

> The resistivity of a semiconductor can be modified by adding different amounts of impurities. A rod of semiconducting material of length L and cross-sectional area A lies along the x-axis between x = 0 and x = L. The material obeys Ohm’s law, and its res

> According to the U.S. National Electrical Code, copper wire used for interior wiring of houses, hotels, office buildings, and industrial plants is permitted to carry no more than a specified maximum amount of current. The table shows values of the maximu

> The voltage drop Vab across each of resistors A and B was measured as a function of the current I in the resistor. The results are shown in the table: (a). For each resistor, graph Vab as a function of I and graph the resistance R = Vab/I as a function

> An external resistor R is connected between the terminals of a battery. The value of R varies. For each R value, the current I in the circuit and the terminal voltage Vab of the battery are measured. The results are plotted in Fig. P25.74, a graph of Vab

> Consider the circuit shown in Fig. P25.73. The emf source has negligible internal resistance. The resistors have resistances R1 = 6.00 Ω and R2 = 4.00 Ω. The capacitor has capacitance C = 9.00 µF. When the capacitor is fully charged, the magnitude of the

> A circular coil with area A and N turns is free to rotate about a diameter that coincides with the x-axis. Current I is circulating in the coil. There is a uniform magnetic field

> Consider the circuit shown in Fig. P25.72. The battery has emf 72.0 V and negligible internal resistance. R2 = 2.00 Ω, C1 = 3.00 µF, and C2 = 6.00 mF. After the capacitors have attained their final charges, the charge on C1 is Q1

> Why should the permeability of a paramagnetic material be expected to decrease with increasing temperature?

> A lightning bolt strikes one end of a steel lightning rod, producing a 15,000-A current burst that lasts for 65 µs. The rod is 2.0 m long and 1.8 cm in diameter, and its other end is connected to the ground by 35 m of 8.0-mm-diameter copper wire. (a). F

> Compact fluorescent bulbs are much more efficient at producing light than are ordinary incandescent bulbs. They initially cost much more, but they last far longer and use much less electricity. According to one study of these bulbs, a compact bulb that p

> A 1.50-m cylinder of radius 1.10 cm is made of a complicated mixture of materials. Its resistivity depends on the distance x from the left end and obeys the formula

> A cylindrical copper cable 1.50 km long is connected across a 220.0-V potential difference. (a). What should be its diameter so that it produces heat at a rate of 90.0 W? (b). What is the electric field inside the cable under these conditions?

> Unlike the idealized ammeter described in Section 25.4, any real ammeter has a nonzero resistance. (a). An ammeter with resistance RA is connected in series with a resistor R and a battery of emf

> In the circuit shown in Fig. P25.66, R is a variable resistor whose value ranges from 0 to ∞, and a and b are the terminals of a battery that has an emf

> A typical cost for electrical power is $0.120 per kilowatthour. (a). Some people leave their porch light on all the time. What is the yearly cost to keep a 75-W bulb burning day and night? (b). Suppose your refrigerator uses 400 W of power when it’s runn

> In the circuit shown in Fig. P26.64,

> Both circular coils A and B (Fig. E27.44) have area A and N turns. They are free to rotate about a diameter that coincides with the x-axis. Current I circulates in each coil in the direction shown. There is a uniform magnetic field

> Consider the circuit shown in Fig. P26.63. Fig. P26.63: (a). What must the emf 10.0 Ω 20.0 Ω ww 60.0 N 60.0 N 2.00 A ww 30.0 2 5.0 Ω 5.0 V 10.0 V 5.00 15.0 N ww- 20.0 N +

> (a). What is the potential difference Vad in the circuit of Fig. P25.62? Fig. P25.62: / / (b). What is the terminal voltage of the 4.00-V battery? (c). A battery with emf 10.30 V and internal resistance 0.50 Ω is inserted in the circuit at d, with i

> A metal ring carries a current that causes a magnetic field B0 at the center of the ring and a field B at point P a distance x from the center along the axis of the ring. If the radius of the ring is doubled, find the magnetic field at the center. Will t

> The potential difference across the terminals of a battery is 8.40 V when there is a current of 1.50 A in the battery from the negative to the positive terminal. When the current is 3.50 A in the reverse direction, the potential difference becomes 10.20

> The region between two concentric conducting spheres with radii a and b is filled with a conducting material with resistivity

> A material of resistivity

> A resistor with resistance R is connected to a battery that has emf 12.0 V and internal resistance r = 0.40 Ω. For what two values of R will the power dissipated in the resistor be 80.0 W?

> Lightning strikes can involve currents as high as 25,000 A that last for about 40 ms. If a person is struck by a bolt of lightning with these properties, the current will pass through his body. We shall assume that his mass is 75 kg, that he is wet (afte

> A heating element made of tungsten wire is connected to a large battery that has negligible internal resistance. When the heating element reaches 80.0oC, it consumes electrical energy at a rate of 480 W. What is its power consumption when its temperature

> A 3.00-m length of copper wire at 20° C has a 1.20-mlong section with diameter 1.60 mm and a 1.80-m-long section with diameter 0.80 mm. There is a current of 2.5 mA in the 1.60- mm-diameter section. (a). What is the current in the 0.80-mmdiameter sectio

> A student claims that if lightning strikes a metal flagpole, the force exerted by the earth’s magnetic field on the current in the pole can be large enough to bend it. Typical lightning currents are of the order of 104 to 105 A. Is the student’s opinion

> A 2.0-m length of wire is made by welding the end of a 120-cm-long silver wire to the end of an 80-cm-long copper wire. Each piece of wire is 0.60 mm in diameter. The wire is at room temperature, so the resistivities are as given in Table 25.1. A potenti

> On your first day at work as an electrical technician, you are asked to determine the resistance per meter of a long piece of wire. The company you work for is poorly equipped. You find a battery, a voltmeter, and an ammeter, but no meter for directly me

> An overhead transmission cable for electrical power is 2000 m long and consists of two parallel copper wires, each encased in insulating material. A short circuit has developed somewhere along the length of the cable where the insulation has worn thin an

> Two very long, parallel wires carry equal currents in opposite directions. (a). Is there any place that their magnetic fields completely cancel? If so, where? If not, why not? (b). How would the answer to part (a) change if the currents were in the sam

> An electrical conductor designed to carry large currents has a circular cross section 2.50 mm in diameter and is 14.0 m long. The resistance between its ends is 0.104 Ω. (a). What is the resistivity of the material? (b). If the electric-field magnitude

> In an ionic solution, a current consists of Ca2+ ions (of charge +2e) and Cl- ions (of charge -e) traveling in opposite directions. If 5.11 × 1018 Cl- ions go from A to B every 0.50 min, while 3.24 × 1018 Ca2+ ions move from B to A, what is the current (

> (a). What would have to be the self-inductance of a solenoid for it to store 10.0 J of energy when a 2.00-A current runs through it? (b). If this solenoid’s cross-sectional diameter is 4.00 cm, and if you could wrap its coils to a density of 10 coils/mm

> In the circuit in Fig. P29.47, an emf of 90.0 V is added in series with the capacitor and the resistor, and the capacitor is initially uncharged. The emf is placed between the capacitor and switch S, with the positive terminal of the emf adjacent to the

> A very long, rectangular loop of wire can slide without friction on a horizontal surface. Initially the loop has part of its area in a region of uniform magnetic field that has magnitude B = 2.90 T and is perpendicular to the plane of the loop. The loop

> A uniform rectangular coil of total mass 212 g and dimensions 0.500 m × 1.00 m is oriented with its plane parallel to a uniform 3.00-T magnetic field (Fig. E27.43). A current of 2.00 A is suddenly started in the coil. Fig. E27.43: (a). A

> Magnetic fields within a sunspot can be as strong as 0.4 T. (By comparison, the earth’s magnetic field is about 1/10,000 as strong.) Sunspots can be as large as 25,000 km in radius. The material in a sunspot has a density of about 3 × 10-4 kg/m3. Assume

> For the circuit of Fig. 30.17, let C = 15.0 nF, L = 22 mH, and R = 75.0 Ω. Fig. 30.17: (a). Calculate the oscillation frequency of the circuit once the capacitor has been charged and the switch has been connected to point a. (b).

> An L-R-C series circuit has L = 0.400 H, C = 7.00 µF, and R = 320 Ω. At t = 0 the current is zero and the initial charge on the capacitor is 2.80 × 10-4 C. (a). What are the values of the constants A and

> The minimum capacitance of a variable capacitor in a radio is 4.18 pF. (a). What is the inductance of a coil connected to this capacitor if the oscillation frequency of the L-C circuit is 1600 × 103 Hz, corresponding to one end of the AM radio broadcast

> What are the relative advantages and disadvantages of Ampere’s law and the law of Biot and Savart for practical calculations of magnetic fields?

> A capacitor with capacitance 6.00 × 10-5 F is charged by connecting it to a 12.0-V battery. The capacitor is disconnected from the battery and connected across an inductor with L = 1.50 H. (a). What are the angular frequency v of the electrical oscillat

> A 18.0-µF capacitor is placed across a 22.5-V battery for several seconds and is then connected across a 12.0-mH inductor that has no appreciable resistance. (a). After the capacitor and inductor are connected together, find the maximum current in the c

> A 7.50-nF capacitor is charged up to 12.0 V, then disconnected from the power supply and connected in series through a coil. The period of oscillation of the circuit is then measured to be 8.60 × 10-5 s. Calculate: (a). the inductance of the coil; (b).

> A 15.0-µF capacitor is charged by a 150.0-V power supply, then disconnected from the power and connected in series with a 0.280-mH inductor. Calculate: (a). the oscillation frequency of the circuit; (b). the energy stored in the capacitor at time t = 0

> In Fig. 30.11, R = 15.0 and the battery emf is 6.30 V. With switch S2 open, switch S1 is closed. After several minutes, S1 is opened and S2 is closed. Fig. 30.11: (a) At 2.00 ms after S1 is opened, the current has decayed to 0.280 A. Calculate the i

> A rectangular coil of wire, 22.0 cm by 35.0 cm and carrying a current of 1.95 A, is oriented with the plane of its loop perpendicular to a uniform 1.50-T magnetic field (Fig. E27.42). Fig. E27.42: (a). Calculate the net force and torque that the magn

> An inductor with an inductance of 2.50 H and a resistance of 8.00 Ω is connected to the terminals of a battery with an emf of 6.00 V and negligible internal resistance. Find (a). the initial rate of increase of current in the circuit; (b). the rate of

> Consider the circuit in Exercise 30.23. Exercise 30.23: An inductor with an inductance of 2.50 H and a resistance of 8.00 Ω is connected to the terminals of a battery with an emf of 6.00 V and negligible internal resistance. Find (a). Just after the

> In Fig. 30.11, suppose that

> In Fig. 30.11, suppose that

> In Fig. 30.11, switch S1 is closed while switch S2 is kept open. The inductance is L = 0.115 H, and the resistance is R = 120 Ω. Fig. 30.11: (a). When the current has reached its final value, the energy stored in the inductor is 0

> How might a loop of wire carrying a current be used as a compass? Could such a compass distinguish between north and south? Why or why not?

> A solenoid 25.0 cm long and with a cross-sectional area of 0.500 cm2 contains 400 turns of wire and carries a current of 80.0 A. Calculate: (a). the magnetic field in the solenoid; (b). the energy density in the magnetic field if the solenoid is filled

> An inductor used in a dc power supply has an inductance of 12.0 H and a resistance of 180 Ω. It carries a current of 0.500 A. (a). What is the energy stored in the magnetic field? (b). At what rate is thermal energy developed in the inductor? (c). Doe

> It is proposed to store 1.00 kW # h = 3.60 × 106 J of electrical energy in a uniform magnetic field with magnitude 0.600 T. (a). What volume (in vacuum) must the magnetic field occupy to store this amount of energy? (b). If instead this amount of energ

> It has been proposed to use large inductors as energy storage devices. (a). How much electrical energy is converted to light and thermal energy by a 150-W light bulb in one day? (b). If the amount of energy calculated in part (a) is stored in an induct

> A straight, 2.5-m wire carries a typical household current of 1.5 A (in one direction) at a location where the earth’s magnetic field is 0.55 gauss from south to north. Find the magnitude and direction of the force that our planet’s magnetic field exerts

> A 2.50-mH toroidal solenoid has an average radius of 6.00 cm and a cross-sectional area of 2.00 cm2. (a). How many coils does it have? (Make the same assumption as in Example 30.3.) (b). At what rate must the current through it change so that a potentia

> A toroidal solenoid has mean radius 12.0 cm and crosssectional area 0.600 cm2. (a). How many turns does the solenoid have if its inductance is 0.100 mH? (b). What is the resistance of the solenoid if the wire from which it is wound has a resistance per

> The inductor shown in Fig. E30.11 has inductance 0.260 H and carries a current in the direction shown. The current is changing at a constant rate. Fig. E30.11: (a). The potential between points a and b is Vab = 1.04 V, with point a at higher potentia

> The inductor in Fig. E30.11 has inductance 0.260 H and carries a current in the direction shown that is decreasing at a uniform rate, di/dt = -0.0180 A/s. Fig. E30.11: (a). Find the self-induced emf. (b). Which end of the inductor, a or b, is at a h

> A toroidal solenoid has 500 turns, cross-sectional area 6.25 cm2, and mean radius 4.00 cm. (a). Calculate the coil’s self-inductance. (b). If the current decreases uniformly from 5.00 A to 2.00 A in 3.00 ms, calculate the self-induced emf in the coil. (

> Two coils are wound around the same cylindrical form, like the coils in Example 30.1. When the current in the first coil is decreasing at a rate of -0.242 A/s, the induced emf in the second coil has magnitude 1.65 × 10-3 V. (a). What is the mutual induc

> At any point in space, the electric field

> A solenoidal coil with 25 turns of wire is wound tightly around another coil with 300 turns (see Example 30.1). The inner solenoid is 25.0 cm long and has a diameter of 2.00 cm. At a certain time, the current in the inner solenoid is 0.120 A and is incre

> A 10.0-cm-long solenoid of diameter 0.400 cm is wound uniformly with 800 turns. A second coil with 50 turns is wound around the solenoid at its center. What is the mutual inductance of the combination of the two coils?

> At temperatures near absolute zero, Bc approaches 0.142 T for vanadium, a type-I superconductor. The normal phase of vanadium has a magnetic susceptibility close to zero. Consider a long, thin vanadium cylinder with its axis parallel to an external magne

> The circuit shown in Fig. E27.39 is used to make a magnetic balance to weigh objects. The mass m to be measured is hung from the center of the bar that is in a uniform magnetic field of 1.50 T, directed into the plane of the figure. The battery voltage c

> (a). What is the speed of a beam of electrons when the simultaneous influence of an electric field of 1.56 × 104 V/m and a magnetic field of 4.62 × 10-3 T, with both fields normal to the beam and to each other, produces no deflection of the electrons? (b

> A singly ionized (one electron removed) 40K atom passes through a velocity selector consisting of uniform perpendicular electric and magnetic fields. The selector is adjusted to allow ions having a speed of 4.50 km/s to pass through undeflected when the

> A 150-V battery is connected across two parallel metal plates of area 28.5 cm2 and separation 8.20 mm. A beam of alpha particles (charge +2e, mass 6.64 × 10-27 kg) is accelerated from rest through a potential difference of 1.75 kV and enters

> An electron at point A in Fig. E27.15 has a speed v0 of 1.41 × 106 m/s. Find Fig. E27.15: (a). the magnitude and direction of the magnetic field that will cause the electron to follow the semicircular path from A to B, and (b). the time

> A singly charged ion of 7Li (an isotope of lithium) has a mass of 1.16 × 10-26 kg. It is accelerated through a potential difference of 220 V and then enters a magnetic field with magnitude 0.874 T perpendicular to the path of the ion. What is the radius

> A proton (q = 1.60 × 10-19 C, m = 1.67 × 10-27 kg) moves in a uniform magnetic field

> A beam of protons traveling at 1.20 km/s enters a uniform magnetic field, traveling perpendicular to the field. The beam exits the magnetic field, leaving the field in a direction perpendicular to its original direction (Fig. E27.24). The beam travels a

> An electron in the beam of a cathode-ray tube is accelerated by a potential difference of 2.00 kV. Then it passes through a region of transverse magnetic field, where it moves in a circular arc with radius 0.180 m. What is the magnitude of the field?

> In a cyclotron, the orbital radius of protons with energy 300 keV is 16.0 cm. You are redesigning the cyclotron to be used instead for alpha particles with energy 300 keV. An alpha particle has charge q = +2e and mass m = 6.64 × 10-27 kg. If the magnetic

> If the battery in Discussion Question Q26.10 is ideal with no internal resistance, what will happen to the brightness of the bulb when S is closed? Why? Discussion Question Q26.10: A real battery, having nonnegligible internal resistance, is connected

> A deuteron (the nucleus of an isotope of hydrogen) has a mass of 3.34 × 10-27 kg and a charge of +e. The deuteron travels in a circular path with a radius of 6.96 mm in a magnetic field with magnitude 2.50 T. (a). Find the speed of the deuteron. (b). F

> Cyclotrons are widely used in nuclear medicine for producing short-lived radioactive isotopes. These cyclotrons typically accelerate H- (the hydride ion, which has one proton and two electrons) to an energy of 5 MeV to 20 MeV. This ion has a mass very cl

> In an experiment with cosmic rays, a vertical beam of particles that have charge of magnitude 3e and mass 12 times the proton mass enters a uniform horizontal magnetic field of 0.250 T and is bent in a semicircle of diameter 95.0 cm, as shown in Fig. E27

> An alpha particle (a He nucleus, containing two protons and two neutrons and having a mass of 6.64 × 10-27 kg) traveling horizontally at 35.6 km/s enters a uniform, vertical, 1.80-T magnetic field. (a). What is the diameter of the path followed by this

> A 150-g ball containing 4.00 × 108 excess electrons is dropped into a 125-m vertical shaft. At the bottom of the shaft, the ball suddenly enters a uniform horizontal magnetic field that has magnitude 0.250 T and direction from east to west. If air resist

> Repeat Exercise 27.15 for the case in which the particle is a proton rather than an electron. Exercise 27.15: An electron at point A in Fig. E27.15 has a speed v0 of 1.41 × 106 m/s. Find Fig. E27.15: A B -10.0 cm-