Question: Two point charges of equal magnitude Q

> For the capacitor network shown in Fig. E24.28, the potential difference across ab is 48 V. Find Fig. E24.28: (a). the total charge stored in this network; (b). the charge on each capacitor; (c). the total energy stored in the network; (d). the en

> You have two identical capacitors and an external potential source. (a). Compare the total energy stored in the capacitors when they are connected to the applied potential in series and in parallel. (b). Compare the maximum amount of charge stored in e

> Two parallel-plate capacitors, identical except that one has twice the plate separation of the other, are charged by the same voltage source. Which capacitor has a stronger electric field between the plates? Which capacitor has a greater charge? Which ha

> A parallel-plate vacuum capacitor has 8.38 J of energy stored in it. The separation between the plates is 2.30 mm. If the separation is decreased to 1.15 mm, what is the energy stored (a). if the capacitor is disconnected from the potential source so the

> Electric eels and electric fish generate large potential differences that are used to stun enemies and prey. These potentials are produced by cells that each can generate 0.10 V. We can plausibly model such cells as charged capacitors. (a). How should th

> Figure E24.14 shows a system of four capacitors, where the potential difference across ab is 50.0 V. Figure E24.14: (a). Find the equivalent capacitance of this system between a and b. (b). How much charge is stored by this combination of capacitors

> Suppose the 3-µF capacitor in Fig. 24.10a were removed and replaced by a different one, and that this changed the equivalent capacitance between points a and b to 8 µF. What would be the capacitance of the replacement capacitor?

> For the system of capacitors shown in Fig. E24.21, a potential difference of 25 V is maintained across ab. Fig. E24.21: (a). What is the equivalent capacitance of this system between a and b? (b). How much charge is stored by this system? (c). How m

> In Fig. E24.20, C1 = 6.00 µF, C2 = 3.00 µF, and C3 = 5.00 µF. The capacitor network is connected to an applied potential Vab. After the charges on the capacitors have reached their final values, the charge on C2 is

> In Fig. 24.9a, let C1 = 3.00 µF, C2 = 5.00 µF, and Vab = +52.0 V. Calculate Fig. 24.9a: (a). the charge on each capacitor and (b). the potential difference across each capacitor. Vab = V C: b

> In Fig. 24.8a, let C1 = 3.00 µF, C2 = 5.00 µF, and Vab = +64.0 V. Calculate Fig. 24.8a: (a). the charge on each capacitor and (b). the potential difference across each capacitor. +Q. C Vac = V1 Vab = V +Q. Vab = V2 b KI-

> In Fig. E24.17, each capacitor has C = 4.00 µF and Vab = +28.0 V. Calculate Fig. E24.17: (a). the charge on each capacitor; (b). the potential difference across each capacitor; (c). the potential difference between points a and d. C,

> For the system of capacitors shown in Fig. E24.16, find the equivalent capacitance (a). between b and c, and (b). between a and c. Fig. E24.16: a =15 pF 9.0 pF ; pF

> Can the potential difference between the terminals of a battery ever be opposite in direction to the emf? If it can, give an example. If it cannot, explain why not.

> A 10.0-µF parallel-plate capacitor with circular plates is connected to a 12.0-V battery. (a). What is the charge on each plate? (b). How much charge would be on the plates if their separation were doubled while the capacitor remained connected to the

> A cylindrical capacitor has an inner conductor of radius 2.2 mm and an outer conductor of radius 3.5 mm. The two conductors are separated by vacuum, and the entire capacitor is 2.8 m long. (a). What is the capacitance per unit length? (b). The potentia

> A spherical capacitor contains a charge of 3.30 nC when connected to a potential difference of 220 V. If its plates are separated by vacuum and the inner radius of the outer shell is 4.00 cm, calculate: (a). the capacitance; (b). the radius of the inne

> A cylindrical capacitor consists of a solid inner conducting core with radius 0.250 cm, surrounded by an outer hollow conducting tube. The two conductors are separated by air, and the length of the cylinder is 12.0 cm. The capacitance is 36.7 pF. (a). Ca

> A 5.00-µF parallel-plate capacitor is connected to a 12.0-V battery. After the capacitor is fully charged, the battery is disconnected without loss of any of the charge on the plates. (a). A voltmeter is connected across the two plates without dischargi

> A metal sphere with radius ra is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius rb. There is charge +q on the inner sphere and charge -q on the outer spherical shell. (a). Calculate the potential V(r) for

> A metal sphere with radius ra = 1.20 cm is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius rb = 9.60 cm. Charge +q is put on the inner sphere and charge -q on the outer spherical shell. The magnitude of q is

> In a certain region of space, the electric potential is given by V = +Ax2y - Bxy2, where A = 5.00 V/m3 and B = 8.00 V/m3. Calculate the magnitude and direction of the electric field at the point in the region that has coordinates x = 2.00 m, y = 0.400 m,

> In a certain region of space, the electric potential is V (x, y, z) = Axy - Bx2 + Cy, where A, B, and C are positive constants. (a). Calculate the x-, y-, and z-components of the electric field. (b). At which points is the electric field equal to zero?

> A very large plastic sheet carries a uniform charge density of -6.00 nC/m2 on one face. (a). As you move away from the sheet along a line perpendicular to it, does the potential increase or decrease? How do you know, without doing any calculations? Does

> A parallel-plate capacitor is charged by being connected to a battery and is kept connected to the battery. The separation between the plates is then doubled. How does the electric field change? The charge on the plates? The total energy? Explain.

> A total electric charge of 3.50 nC is distributed uniformly over the surface of a metal sphere with a radius of 24.0 cm. If the potential is zero at a point at infinity, find the value of the potential at the following distances from the center of the sp

> Thin spherical shell with radius R1 = 3.00 cm is concentric with a larger thin spherical shell with radius R2 = 5.00 cm. Both shells are made of insulating material. The smaller shell has charge q1 = +6.00 nC distributed uniformly over its surface, and t

> (a). How much excess charge must be placed on a copper sphere 25.0 cm in diameter so that the potential of its center, relative to infinity, is 3.75 kV? (b). What is the potential of the sphere’s surface relative to infinity?

> The electric field at the surface of a charged, solid, copper sphere with radius 0.200 m is 3800 N/C, directed toward the center of the sphere. What is the potential at the center of the sphere, if we take the potential to be zero infinitely far from the

> Two large, parallel, metal plates carry opposite charges of equal magnitude. They are separated by 45.0 mm, and the potential difference between them is 360 V. (a). What is the magnitude of the electric field (assumed to be uniform) in the region betwee

> Two large, parallel conducting plates carrying opposite charges of equal magnitude are separated by 2.20 cm. (a). If the surface charge density for each plate has magnitude 47.0 nC/m2, what is the magnitude of

> A very small sphere with positive charge q = +8.00 µC is released from rest at a point 1.50 cm from a very long line of uniform linear charge density λ = +3.00 µC/m. What is the kinetic energy of the sphere when it is 4.50 cm from the line of charge if t

> A ring of diameter 8.00 cm is fixed in place and carries a charge of +5.00 µC uniformly spread over its circumference. (a). How much work does it take to move a tiny +3.00-µC charged ball of mass 1.50 g from very far away to the center of the ring? (b).

> A very long insulating cylindrical shell of radius 6.00 cm carries charge of linear density 8.50 µC/m spread uniformly over its outer surface. What would a voltmeter read if it were connected between. (a). the surface of the cylinder and a point 4.00 cm

> A very long insulating cylinder of charge of radius 2.50 cm carries a uniform linear density of 15.0 nC/m. If you put one probe of a voltmeter at the surface, how far from the surface must the other probe be placed so that the voltmeter reads 175 V?

> In the parallel-plate capacitor of Fig. 24.2, suppose the plates are pulled apart so that the separation d is much larger than the size of the plates. Fig. 24.2: (a) Is it still accurate to say that the electric field between the plates is uniform? W

> A very long wire carries a uniform linear charge density λ. Using a voltmeter to measure potential difference, you find that when one probe of the meter is placed 2.50 cm from the wire and the other probe is 1.00 cm farther from the wire, the meter reads

> An infinitely long line of charge has linear charge density 5.00 × 10-12 C/m. A proton (mass 1.67 ×10-27 kg, charge +1.60 × 10-19 C) is 18.0 cm from the line and moving directly toward the line at 3.50 × 103 m/s. (a). Calculate the proton’s initial kine

> Charge Q = 5.00

> A solid conducting sphere has net positive charge and radius R = 0.400 m. At a point 1.20 m from the center of the sphere, the electric potential due to the charge on the sphere is 24.0 V. Assume that V = 0 at an infinite distance from the sphere. What i

> A uniformly charged, thin ring has radius 15.0 cm and total charge +24.0 nC. An electron is placed on the ring’s axis a distance 30.0 cm from the center of the ring and is constrained to stay on the axis of the ring. The electron is then released from re

> A particle with charge +4.20 nC is in a uniform electric field

> An object with charge q = -6.00 × 10-9 C is placed in a region of uniform electric field and is released from rest at point A. After the charge has moved to point B, 0.500 m to the right, it has kinetic energy 3.00 × 10-7 J. (a). If the electric potenti

> For each of the following arrangements of two point charges, find all the points along the line passing through both charges for which the electric potential V is zero (take V = 0 infinitely far from the charges) and for which the electric field E is zer

> A uniform electric field has magnitude E and is directed in the negative x-direction. The potential difference between point a (at x = 0.60 m) and point b (at x = 0.90 m) is 240 V. (a). Which point, a or b, is at the higher potential? (b). Calculate the

> At a certain distance from a point charge, the potential and electric-field magnitude due to that charge are 4.98 V and 16.2 V/m, respectively. (Take V = 0 at infinity.) (a). What is the distance to the point charge? (b). What is the magnitude of the c

> Two copper wires with different diameters are joined end to end. If a current flows in the wire combination, what happens to electrons when they move from the larger-diameter wire into the smaller-diameter wire? Does their drift speed increase, decrease,

> (a). An electron is to be accelerated from 3.00 × 106 m/s to 8.00 × 106 m/s. Through what potential difference must the electron pass to accomplish this? (b). Through what potential difference must the electron pass if it is to be slowed from 8.00 × 106

> Two point charges q1 = +2.40 nC and q2 = -6.50 nC are 0.100 m apart. Point A is midway between them; point B is 0.080 m from q1 and 0.060 m from q2 (Fig. E23.19). Take the electric potential to be zero at infinity. Find Figure E23.19: (a). the potent

> Point charges q1 = +2.00 µC and q2 = -2.00 µC are placed at adjacent corners of a square for which the length of each side is 3.00 cm. Point a is at the center of the square, and point b is at the empty corner closest to q2. Take the electric potential t

> Two stationary point charges +3.00 nC and +2.00 nC are separated by a distance of 50.0 cm. An electron is released from rest at a point midway between the two charges and moves along the line connecting the two charges. What is the speed of the electron

> A charge of 28.0 nC is placed in a uniform electric field that is directed vertically upward and has a magnitude of 4.00 × 104 V/m. What work is done by the electric force when the charge moves (a). 0.450 m to the right; (b). 0.670 m upward; (c). 2.60

> (a). How much work would it take to push two protons very slowly from a separation of 2.00 × 10-10 m (a typical atomic distance) to 3.00 × 10-15 m (a typical nuclear distance)? (b). If the protons are both released from rest at the closer distance in pa

> A point charge q1 is held stationary at the origin. A second charge q2 is placed at point a, and the electric potential energy of the pair of charges is +5.4 × 10-8 J. When the second charge is moved to point b, the electric force on the charge does -1.9

> Three point charges, which initially are infinitely far apart, are placed at the corners of an equilateral triangle with sides d. Two of the point charges are identical and have charge q. If zero network is required to place the three charges at the corn

> Four electrons are located at the corners of a square 10.0 nm on a side, with an alpha particle at its midpoint. How much work is needed to move the alpha particle to the midpoint of one of the sides of the square?

> How much work is needed to assemble an atomic nucleus containing three protons (such as Li) if we model it as an equilateral triangle of side 2.00 × 10-15 m with a proton at each vertex? Assume the protons started from very far away.

> Two protons are released from rest when they are 0.750 nm apart. (a). What is the maximum speed they will reach? When does this speed occur? (b). What is the maximum acceleration they will achieve? When does this acceleration occur?

> Three equal 1.20-µC point charges are placed at the corners of an equilateral triangle with sides 0.400 m long. What is the potential energy of the system? (Take as zero the potential energy of the three charges when they are infinitely far apart.)

> Two protons, starting several meters apart, are aimed directly at each other with speeds of 2.00 × 105 m/s, measured relative to the earth. Find the maximum electric force that these protons will exert on each other.

> (a). Calculate the electric potential energy of the adenine–thymine bond, using the same combinations of molecules (O-H-N and N-H-N) as in Exercise 21.21. Exercise 21.21: (a). Calculate the net force that thymine exerts on adenine. Is it attractive or

> When is a 1.5-V AAA battery not actually a 1.5-V battery? That is, when do its terminals provide a potential difference of less than 1.5 V?

> To store the maximum amount of energy in a parallelplate capacitor with a given battery (voltage source), would it be better to have the plates far apart or close together?

> Suppose the two plates of a capacitor have different areas. When the capacitor is charged by connecting it to a battery, do the charges on the two plates have equal magnitude, or may they be different? Explain your reasoning.

> A cylindrical rod has resistance R. If we triple its length and diameter, what is its resistance, in terms of R?

> Equation (24.2) shows that the capacitance of a parallelplate capacitor becomes larger as the plate separation d decreases. However, there is a practical limit to how small d can be made, which places limits on how large C can be. Explain what sets the l

> The maximum voltage at the center of a typical tandem electrostatic accelerator is 6.0 MV. If the distance from one end of the acceleration tube to the midpoint is 12 m, what is the magnitude of the average electric field in the tube under these conditio

> The electric potential V in a region of space is given by where A is a constant. (a). Derive an expression for the electric field E S at any point in this region. (b). The work done by the field when a 1.50-µC test charge moves from the

> Two plastic spheres, each carrying charge uniformly distributed throughout its interior, are initially placed in contact and then released. One sphere is 60.0 cm in diameter, has mass 50.0 g, and contains -10.0 µC of charge. The other sphere is 40.0 cm i

> A thin insulating rod is bent into a semicircular arc of radius a, and a total electric charge Q is distributed uniformly along the rod. Calculate the potential at the center of curvature of the arc if the potential is assumed to be zero at infinity.

> Three square metal plates A, B, and C, each 12.0 cm on a side and 1.50 mm thick, are arranged as in Fig. P24.67. The plates are separated by sheets of paper 0.45 mm thick and with dielectric constant 4.2. The outer plates are connected together and conne

> A parallel-plate capacitor has square plates that are 8.00 cm on each side and 3.80 mm apart. The space between the plates is completely filled with two square slabs of dielectric, each 8.00 cm on a side and 1.90 mm thick. One slab is Pyrex glass and the

> The inner cylinder of a long, cylindrical capacitor has radius ra and linear charge density +λ. It is surrounded by a coaxial cylindrical conducting shell with inner radius rb and linear charge density -λ (see Fig. 24.6). Fig.

> A Geiger counter detects radiation such as alpha particles by using the fact that the radiation ionizes the air along its path. A thin wire lies on the axis of a hollow metal cylinder and is insulated from it (Fig. P23.62). A large potential difference i

> The charge center of a thundercloud, drifting 3.0 km above the earth’s surface, contains 20 C of negative charge. Assuming the charge center has a radius of 1.0 km, and modeling the charge center and the earth’s surface as parallel plates, calculate: (a

> (a). Calculate the potential energy of a system of two small spheres, one carrying a charge of 2.00 µC and the other a charge of -3.50 µC, with their centers separated by a distance of 0.180 m. Assume that U = 0 when the charges are infinitely separated.

> 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