Question: A student asked, “Since electrical potential is

> If the power plant uses a Carnot cycle and the desired theoretical efficiency is 6.5%, from what depth must cold water be brought? (a). 100 m; (b). 400 m; (c). 800 m; (d). deeper than 1000 m.

> Consider a Diesel cycle that starts (at point a in Fig. 20.7) with air at temperature Ta. The air may be treated as an ideal gas. Fig. 20.7: (a). If the temperature at point c is Tc, derive an expression for the efficiency of the cycle in terms of th

> A very long, straight wire has charge per unit length 3.20 × 10-10 C/m. At what distance from the wire is the electric field magnitude equal to 2.50 N/C?

> A Carnot engine operates between two heat reservoirs at temperatures TH and TC. An inventor proposes to increase the efficiency by running one engine between TH and an intermediate temperature T′ and a second engine between T′ and TC, using as input the

> A nerve signal is transmitted through a neuron when an excess of Na+ ions suddenly enters the axon, a long cylindrical part of the neuron. Axons are approximately 10.0 mm in diameter, and measurements show that about 5.6 × 1011 Na+ ions per meter (each o

> We often say that if point A is at a higher potential than point B, A is at positive potential and B is at negative potential. Does it necessarily follow that a point at positive potential is positively charged, or that a point at negative potential is n

> Point charge q1 = -5.00 nC is at the origin and point charge q2 = +3.00 nC is on the x-axis at x = 3.00 cm. Point P is on the y-axis at y = 4.00 cm. (a). Calculate the electric fields

> A point charge is placed at each corner of a square with side length a. All charges have magnitude q. Two of the charges are positive and two are negative (Fig. E21.42). What is the direction of the net electric field at the center of the square due to t

> The nuclei of large atoms, such as uranium, with 92 protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately 7.4 × 10-15 m. (a). What is the electric field this nucleus produces just outside i

> The cube in Fig. E22.6 has sides of length L = 10.0 cm. The electric field is uniform, has magnitude E = 4.00 × 103 N/C, and is parallel to the xy-plane at an angle of 53.1 measured from the +x-axis toward the +y-axis. Figure E22.6: (a).

> A point charge is at the origin. With this point charge as the source point, what is the unit vector

> A particle has charge -5.00 nC. (a). Find the magnitude and direction of the electric field due to this particle at a point 0.250 m directly above it. (b). At what distance from this particle does its electric field have a magnitude of 12.0 N/C?

> An average human weighs about 650 N. If each of two average humans could carry 1.0 C of excess charge, one positive and one negative, how far apart would they have to be for the electric attraction between them to equal their 650-N weight?

> Two small spheres spaced 20.0 cm apart have equal charge. How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is 3.33 × 10-21 N?

> In Example 21.4, what is the net force (magnitude and direction) on charge q1 exerted by the other two charges?

> A cube has sides of length L = 0.300 m. One corner is at the origin (Fig. E22.6). The nonuniform electric field is given by

> A uniform electric field is directed due east. Point B is 2.00 m west of point A, point C is 2.00 m east of point A, and point D is 2.00 m south of A. For each point, B, C, and D, is the potential at that point larger, smaller, or the same as at point A?

> An ideal Carnot engine operates between 5000C and 1000C with a heat input of 250 J per cycle. (a). How much heat is delivered to the cold reservoir in each cycle? (b). What minimum number of cycles is necessary for the engine to lift a 500-kg rock thro

> Three point charges are arranged on a line. Charge q3 = +5.00 nC and is at the origin. Charge q2 = -3.00 nC and is at x = +4.00 cm. Charge q1 is at x = +2.00 cm. What is q1 (magnitude and sign) if the net force on q3 is zero?

> A lonely party balloon with a volume of 2.40 L and containing 0.100 mol of air is left behind to drift in the temporarily uninhabited and depressurized International Space Station. Sunlight coming through a porthole heats and explodes the balloon, causin

> A negative charge of -0.550 µC exerts an upward 0.600-N force on an unknown charge that is located 0.300 m directly below the first charge. What are (a). the value of the unknown charge (magnitude and sign); (b). the magnitude and direction of the forc

> A sophomore with nothing better to do adds heat to 0.350 kg of ice at 0.00C until it is all melted. (a). What is the change in entropy of the water? (b). The source of heat is a very massive body at 25.00C. What is the change in entropy of this body? (

> You design an engine that takes in 1.50 × 104 J of heat at 650 K in each cycle and rejects heat at a temperature of 290 K. The engine completes 240 cycles in 1 minute. What is the theoretical maximum power output of your engine, in horsepower?

> A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. In 5 minutes of operation, the heat rejected by the engine melts 0.0400 kg of ice. During this time,

> A Carnot engine whose high-temperature reservoir is at 620 K takes in 550 J of heat at this temperature in each cycle and gives up 335 J to the low-temperature reservoir. (a). How much mechanical work does the engine perform during each cycle? What is

> A Carnot engine is operated between two heat reservoirs at temperatures of 520 K and 300 K. (a). If the engine receives 6.45 kJ of heat energy from the reservoir at 520 K in each cycle, how many joules per cycle does it discard to the reservoir at 300 K

> A conductor that carries a net charge Q has a hollow, empty cavity in its interior. Does the potential vary from point to point within the material of the conductor? What about within the cavity? How does the potential inside the cavity compare to the po

> It is easy to produce a potential difference of several thousand volts between your body and the floor by scuffing your shoes across a nylon carpet. When you touch a metal doorknob, you get a mild shock. Yet contact with a power line of comparable voltag

> The air temperature and the velocity of the air have different values at different places in the earth’s atmosphere. Is the air velocity a vector field? Why or why not? Is the air temperature a vector field? Again, why or why not?

> The electric fields at point P due to the positive charges q1 and q2 are shown in Fig. Q21.22. Does the fact that they cross each other violate the statement in Section 21.6 that electric field lines never cross? Explain. Figure Q21.22: 42

> Sufficiently strong electric fields can cause atoms to become positively ionized—that is, to lose one or more electrons. Explain how this can happen. What determines how strong the field must be to make this happen?

> Atomic nuclei are made of protons and neutrons. This shows that there must be another kind of interaction in addition to gravitational and electric forces. Explain.

> Two irregular objects A and B carry charges of opposite sign. Figure Q21.19 shows the electric field lines near each of these objects. Figure Q21.19: (a). Which object is positive, A or B? How do you know? (b). Where is the electric field stronger,

> In electronics it is customary to define the potential of ground (thinking of the earth as a large conductor) as zero. Is this consistent with the fact that the earth has a net electric charge that is not zero?

> In Example 21.1 (Section 21.3) we saw that the electric force between two

> Because electric field lines and equipotential surfaces are always perpendicular, two equipotential surfaces can never cross; if they did, the direction of

> A point charge of mass m and charge Q and another point charge of mass m but charge 2Q are released on a frictionless table. If the charge Q has an initial acceleration a0, what will be the acceleration of 2Q: a0, 2a0, 4a0, a0/2, or a0/4? Explain.

> If the electric potential at a single point is known, can

> The potential difference between the two terminals of an AA battery (used in flashlights and portable stereos) is 1.5 V. If two AA batteries are placed end to end with the positive terminal of one battery touching the negative terminal of the other, what

> You have a negatively charged object. How can you use it to place a net negative charge on an insulated metal sphere? To place a net positive charge on the sphere?

> If you walk across a nylon rug and then touch a large metal object such as a doorknob, you may get a spark and a shock. Why does this tend to happen more on dry days than on humid days? (Hint: See Fig. 21.30.) Why are you less likely to get a shock if yo

> A diesel engine performs 2200 J of mechanical work and discards 4300 J of heat each cycle. (a). How much heat must be supplied to the engine in each cycle? (b). What is the thermal efficiency of the engine?

>   If E ⃗ is zero throughout a certain region of space, is the potential necessarily also zero in this region? Why or why not? If not, what can be said about the potential?

> In a conductor, one or more electrons from each atom are free to roam throughout the volume of the conductor. Does this contradict the statement that any excess charge on a solid conductor must reside on its surface? Why or why not?

> Good conductors of electricity, such as metals, are typically good conductors of heat; insulators, such as wood, are typically poor conductors of heat. Explain why there is a relationship between conduction of electricity and conduction of heat in these

> Since potential can have any value you want depending on the choice of the reference level of zero potential, how does a voltmeter know what to read when you connect it between two points?

> You find a sealed box on your doorstep. You suspect that the box contains several charged metal spheres packed in insulating material. How can you determine the total net charge inside the box without opening the box? Or isn’t this possible?

> In Fig. 22.15, suppose a third point charge were placed outside the purple Gaussian surface C. Would this affect the electric flux through any of the surfaces A, B, C, or D in the figure? Why or why not? Fig. 22.15: D.

> A certain region of space bounded by an imaginary closed surface contains no charge. Is the electric field always zero everywhere on the surface? If not, under what circumstances is it zero on the surface?

> The electric force between two charged particles becomes weaker with increasing distance. Suppose instead that the electric force were independent of distance. In this case, would a charged comb still cause a neutral insulator to become polarized as in F

> Suppose that in Fig. 22.15 both charges were positive. What would be the fluxes through each of the four surfaces in the example? Fig. 22.15: D.

> A rubber balloon has a single point charge in its interior. Does the electric flux through the balloon depend on whether or not it is fully inflated? Explain your reasoning.

> Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities s1, s2, s3, and s4 on their surfaces (Fig. E22.30). These surface charge densities have the values s1 = -6.00 µC/m2, s2 = +5.00 µC/

> An infinitely long cylindrical conductor has radius R and uniform surface charge density

> A square insulating sheet 80.0 cm on a side is held horizontally. The sheet has 4.50 nC of charge spread uniformly over its area. (a). Calculate the electric field at a point 0.100 mm above the center of the sheet. (b). Estimate the electric field at a

> Apply Gauss’s law to the Gaussian surfaces S2 , S3 , and S4 in Fig. 22.21b to calculate the electric field between and outside the plates. Fig. 22.21b: (b) Idealized model 1 In the idealized case we ignore "fringing" at the plate

> A very large, horizontal, nonconducting sheet of charge has uniform charge per unit area s = 5.00 × 10-6 C/m2. (a). A small sphere of mass m = 8.00 × 10-6 kg and charge q is placed 3.00 cm above the sheet of charge and then released from rest. (a). If t

> A conductor with an inner cavity, like that shown in Fig. 22.23c, carries a total charge of +5.00 nC. The charge within the cavity, insulated from the conductor, is -6.00 nC. How much charge is on Fig. 22.23c: (a). the inner surface of the conductor

> Charge Q is distributed uniformly throughout the volume of an insulating sphere of radius R = 4.00 cm. At a distance of r = 8.00 cm from the center of the sphere, the electric field due to the charge distribution has magnitude E = 940 N/C. What are (a).

> A solid copper sphere has a net positive charge. The charge is distributed uniformly over the surface of the sphere, and the electric field inside the sphere is zero. Then a negative point charge outside the sphere is brought close to the surface of the

> An electron is released from rest at a distance of 0.300 m from a large insulating sheet of charge that has uniform surface charge density +2.90 × 10-12 C/m2. (a). How much work is done on the electron by the electric field of the sheet as the electron

> A point charge of -3.00 µC is located in the center of a spherical cavity of radius 6.50 cm that, in turn, is at the center of an insulating charged solid sphere. The charge density in the solid is

> The electric field at a distance of 0.145 m from the surface of a solid insulating sphere with radius 0.355 m is 1750 N/C. (a). Assuming the sphere’s charge is uniformly distributed, what is the charge density inside it? (b). Calculate the electric field

> (a) At a distance of 0.200 cm from the center of a charged conducting sphere with radius 0.100 cm, the electric field is 480 N/C. What is the electric field 0.600 cm from the center of the sphere? (b) At a distance of 0.200 cm from the axis of a very lo

> A hollow, conducting sphere with an outer radius of 0.250 m and an inner radius of 0.200 m has a uniform surface charge density of +6.37 × 10-6 C/m2. A charge of -0.500 µC is now introduced at the center of the cavity inside the sphere. (a). What is the

> The electric field 0.400 m from a very long uniform line of charge is 840 N/C. How much charge is contained in a 2.00-cm section of the line?

> A very long uniform line of charge has charge per unit length 4.80 µC/m and lies along the x-axis. A second long uniform line of charge has charge per unit length -2.40 µC/m and is parallel to the x-axis at y = 0.400 m. What is the net electric field (ma

> Some planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of -3.63 × 1016 N ∙ m2/C at the planet’s surface. Calculate: (a). the total electric charge on the p

> How many excess electrons must be added to an isolated spherical conductor 26.0 cm in diameter to produce an electric field of magnitude 1150 N/C just outside the surface?

> A solid metal sphere with radius 0.450 m carries a net charge of 0.250 nC. Find the magnitude of the electric field (a). at a point 0.100 m outside the surface of the sphere and (b). at a point inside the sphere, 0.100 m below the surface.

> A spherical Gaussian surface encloses a point charge q. If the point charge is moved from the center of the sphere to a point away from the center, does the electric field at a point on the surface change? Does the total flux through the Gaussian surface

> Two very long uniform lines of charge are parallel and are separated by 0.300 m. Each line of charge has charge per unit length +5.20 µC/m. What magnitude of force does one line of charge exert on a 0.0500-m section of the other line of charge?

> A 6.20-µC point charge is at the center of a cube with sides of length 0.500 m. (a). What is the electric flux through one of the six faces of the cube? (b). How would your answer to part (a) change if the sides were 0.250 m long? Explain.

> A point charge q1 = 4.00 nC is located on the x-axis at x = 2.00 m, and a second point charge q2 = -6.00 nC is on the y-axis at y = 1.00 m. What is the total electric flux due to these two point charges through a spherical surface centered at the origin

> A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 12.0 cm, giving it a charge of -49.0 µC. Find the electric field (a). just inside the paint layer; (b). just outside the paint layer; (c). 5.00 cm

> The three small spheres shown in Fig. E22.8 carry charges q1 = 4.00 nC, q2 = -7.80 nC, and q3 = 2.40 nC. Find the net electric flux through each of the following closed surfaces shown in cross section in the figure: Figure E22.8; (a). S1 ; (b). S2 ;

> As discussed in Section 22.5, human nerve cells have a net negative charge and the material in the interior of the cell is a good conductor. If a cell has a net charge of -8.65 pC, what are the magnitude and direction (inward or outward) of the net flux

> A hemispherical surface with radius r in a region of uniform electric field

> It was shown in Example 21.10 (Section 21.5) that the electric field due to an infinite line of charge is perpendicular to the line and has magnitude E = λ /2

> You measure an electric field of 1.25 × 106 N/C at a distance of 0.150 m from a point charge. There is no other source of electric field in the region other than this point charge. (a). What is the electric flux through the surface of a sphere that has

> flat sheet is in the shape of a rectangle with sides of lengths 0.400 m and 0.600 m. The sheet is immersed in a uniform electric field of magnitude 90.0 N/C that is directed at 20 from the plane of the sheet (Fig. E22.2). Find the magnitude of the electr

> A negative charge -Q is placed inside the cavity of a hollow metal solid. The outside of the solid is grounded by connecting a conducting wire between it and the earth. Is any excess charge induced on the inner surface of the metal? Is there any excess c

> A flat sheet of paper of area 0.250 m2 is oriented so that the normal to the sheet is at an angle of 60 to a uniform electric field of magnitude 14 N/C. (a). Find the magnitude of the electric flux through the sheet. (b). Does the answer to part (a) d

> Three charges are at the corners of an isosceles triangle as shown in Fig. E21.57. The {±5.00-µC charges form a dipole. Figure E21.57: (a). Find the force (magnitude and direction) the -10.00-µC charge exerts on

> The dipole moment of the water molecule (H2O) is 6.17 × 10-30 C ∙ m. Consider a water molecule located at the origin whose dipole moment

> An electric dipole with dipole moment

> The ammonia molecule (NH3) has a dipole moment of 5.0 × 10-30 C ∙ m. Ammonia molecules in the gas phase are placed in a uniform electric field

> Point charges q1 = -4.5 nC and q2 = +4.5 nC are separated by 3.1 mm, forming an electric dipole. (a). Find the electric dipole moment (magnitude and direction). (b). The charges are in a uniform electric field whose direction makes an angle of 36.9° wi

> A straight, nonconducting plastic wire 8.50 cm long carries a charge density of +175 nC/m distributed uniformly along its length. It is lying on a horizontal tabletop. (a). Find the magnitude and direction of the electric field this wire produces at a p

> A ring-shaped conductor with radius a = 2.50 cm has a total positive charge Q = +0.125 nC uniformly distributed around it (see Fig. 21.23). The center of the ring is at the origin of coordinates O. Fig. 21.23: (a). What is the electric field (magnitu

> A charge of -6.50 nC is spread uniformly over the surface of one face of a nonconducting disk of radius 1.25 cm. (a). Find the magnitude and direction of the electric field this disk produces at a point P on the axis of the disk a distance of 2.00 cm fro

> A point charge q1 = -4.00 nC is at the point x = 0.600 m, y = 0.800 m, and a second point charge q2 = +6.00 nC is at the point x = 0.600 m, y = 0. Calculate the magnitude and direction of the net electric field at the origin due to these two point charge

> In a certain region of space, the electric field

> Two metal spheres are hanging from nylon threads. When you bring the spheres close to each other, they tend to attract. Based on this information alone, discuss all the possible ways that the spheres could be charged. Is it possible that after the sphere

> In a rectangular coordinate system, a positive point charge q = 6.00 × 10-9 C is placed at the point x = +0.150 m, y = 0, and an identical point charge is placed at x = -0.150 m, y = 0. Find the x- and y-components, the magnitude, and the direction of th

> If two electrons are each 1.50 × 10-10 m from a proton (Fig. E21.45), find the magnitude and direction of the net electric force they will exert on the proton. Fig. E21.45: ! 65.0°

> Two point charges are separated by 25.0 cm (Fig. E21.43). Find the net electric field these charges produce at Fig. E21.43: (a). point A and (b). point B. (c). What would be the magnitude and direction of the electric force this combination of charg

> Three negative point charges lie along a line as shown in Fig. E21.41. Find the magnitude and direction of the electric field this combination of charges produces at point P, which lies 6.00 cm from the -2.00-mC charge measured perpendicular to the line

> Repeat Exercise 21.39, but now let the charge at the origin be -4.00 nC. Exercise 21.39: A +2.00-nC point charge is at the origin, and a second -5.00-nC point charge is on the x-axis at x = 0.800 m.

> A +2.00-nC point charge is at the origin, and a second -5.00-nC point charge is on the x-axis at x = 0.800 m. (a). Find the electric field (magnitude and direction) at each of the following points on the x-axis: (i) x = 0.200 m; (ii) x = 1.20 m; (iii)