A proton is placed in a uniform electric field of 2.75 × 103 N/C. Calculate (a). the magnitude of the electric force felt by the proton; (b). the proton’s acceleration; (c). the proton’s speed after 1.00 ms in the field, assuming it starts from rest.
> 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)
> The two charges q1 and q2 shown in Fig. E21.38 have equal magnitudes. What is the direction of the net electric field due to these two charges at points A (midway between the charges), B, and C if. Fig. E21.38: (a). both charges are negative, (b). b
> Two positive point charges q are placed on the x-axis, one at x = a and one at x = -a. (a). Find the magnitude and direction of the electric field at x = 0. (b). Derive an expression for the electric field at points on the x-axis. Use your result to gr
> Two point charges Q and +q (where q is positive) produce the net electric field shown at point P in Fig. E21.36. The field points parallel to the line connecting the two charges. Fig. E21.36: (a). What can you conclude about the sign and magnitude of
> (a). An electron is moving east in a uniform electric field of 1.50 N/C directed to the west. At point A, the velocity of the electron is 4.50 × 105 m/s toward the east. What is the speed of the electron when it reaches point B, 0.375 m east of point A?
> A lightning rod is a rounded copper rod mounted on top of a building and welded to a heavy copper cable running down into the ground. Lightning rods are used to protect houses and barns from lightning; the lightning current runs through the copper rather
> A +8.75-mC point charge is glued down on a horizontal frictionless table. It is tied to a -6.50-mC point charge by a light, nonconducting 2.50-cm wire. A uniform electric field of magnitude 1.85 × 108 N/C is directed parallel to the wire, as
> A uniform electric field exists in the region between two oppositely charged plane parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate, 1.60 cm distant from the firs
> In Exercise 21.29, what is the speed of the electron as it emerges from the field? Exercise 21.29: An electron is projected with an initial speed v0 = 1.60 × 106 m/s into the uniform field between two parallel plates (Fig. E21.29). Assume
> (a). Calculate the magnitude and direction (relative to the +x-axis) of the electric field in Example 21.6. (b). A -2.5-nC point charge is placed at point P in Fig. 21.19. Find the magnitude and direction of (i) the force that the -8.0-nC charge at the
> An electron is projected with an initial speed v0 = 1.60 × 106 m/s into the uniform field between two parallel plates (Fig. E21.29). Assume that the field between the plates is uniform and directed vertically downward and that the field outs
> The earth has a net electric charge that causes a field at points near its surface equal to 150 N/C and directed in toward the center of the earth. (a). What magnitude and sign of charge would a 60-kg human have to acquire to overcome his or her weight
> (a). What must the charge (sign and magnitude) of a 1.45-g particle be for it to remain stationary when placed in a downward-directed electric field of magnitude 650 N/C? (b). What is the magnitude of an electric field in which the electric force on a p
> An electron is released from rest in a uniform electric field. The electron accelerates vertically upward, traveling 4.50 m in the first 3.00 µs after it is released. (a). What are the magnitude and direction of the electric field? (b). Are we justifie
> A proton is traveling horizontally to the right at 4.50 × 106 m/s. (a). Find the magnitude and direction of the weakest electric field that can bring the proton uniformly to rest over a distance of 3.20 cm. (b). How much time does it take the proton to
> What similarities do electric forces have with gravitational forces? What are the most significant differences?
> Refer to Exercise 21.21. Figure E21.22 shows the bonding of cytosine and guanine. The O—H and H—N distances are each 0.110 nm. In this case, assume that the bonding is due only to the forces along the Oâ€
> The two sides of the DNA double helix are connected by pairs of bases (adenine, thymine, cytosine, and guanine). Because of the geometric shape of these molecules, adenine bonds with thymine and cytosine bonds with guanine. Figure E21.21 shows the bondin
> Two point charges are placed on the x-axis as follows: Charge q1 = +4.00 nC is located at x = 0.200 m, and charge q2 = +5.00 nC is at x = -0.300 m. What are the magnitude and direction of the total force exerted by these two charges on a negative point c
> Two point charges are located on the y-axis as follows: charge q1 = -1.50 nC at y = -0.600 m, and charge q2 = +3.20 nC at the origin (y = 0). What is the total force (magnitude and direction) exerted by these two charges on a third charge q3 = +5.00 nC l
> Repeat Exercise 21.17 for q3 = +8.00 µC. Exercise 21.17: Three point charges are arranged along the x-axis. Charge q1 = +3.00 µC is at the origin, and charge q2 = -5.00 µC is at x = 0.200 m. Charge q3 = -8.00 µC. Where is q3 located if the net force on
> Three point charges are arranged along the x-axis. Charge q1 = +3.00 µC is at the origin, and charge q2 = -5.00 µC is at x = 0.200 m. Charge q3 = -8.00 µC. Where is q3 located if the net force on q1 is 7.00 N in the –x-direction?
> In Example 21.3, calculate the net force on charge q1.
> In Example 21.4, suppose the point charge on the y-axis at y = -0.30 m has negative charge -2.0 µC, and the other charges remain the same. Find the magnitude and direction of the net force on Q. How does your answer differ from that in Example 21.4? Expl
> In an experiment in space, one proton is held fixed and another proton is released from rest a distance of 2.50 mm away. (a). What is the initial acceleration of the proton after it is released? (b). Sketch qualitative (no numbers!) acceleration–time a
> Suppose you had two small boxes, each containing 1.0 g of protons. (a). If one were placed on the moon by an astronaut and the other were left on the earth, and if they were connected by a very light (and very long!) string, what would be the tension in
> You charge up the Van de Graaff generator shown in Fig. 22.26, and then bring an identical but uncharged hollow conducting sphere near it, without letting the two spheres touch. Sketch the distribution of charges on the second sphere. What is the net flu
> Two small plastic spheres are given positive electric charges. When they are 15.0 cm apart, the repulsive force between them has magnitude 0.220 N. What is the charge on each sphere? (a). if the two charges are equal and (b). if one sphere has four time
> Two small aluminum spheres, each having mass 0.0250 kg, are separated by 80.0 cm. (a). How many electrons does each sphere contain? (The atomic mass of aluminum is 26.982 g/mol, and its atomic number is 13.) (b). How many electrons would have to be rem
> Neurons are components of the nervous system of the body that transmit signals as electric impulses travel along their length. These impulses propagate when charge suddenly rushes into and then out of a part of the neuron called an axon. Measurements hav
> You have a pure (24-karat) gold ring of mass 10.8 g. Gold has an atomic mass of 197 g/mol and an atomic number of 79. (a). How many protons are in the ring, and what is their total positive charge? (b). If the ring carries no net charge, how many elect
> If a proton and an electron are released when they are 2.0 × 10-10 m apart (a typical atomic distance), find the initial acceleration of each particle.
> Lightning occurs when there is a flow of electric charge (principally electrons) between the ground and a thundercloud. The maximum rate of charge flow in a lightning bolt is about 20,000 C/s; this lasts for 100 ms or less. How much charge flows between
> Excess electrons are placed on a small lead sphere with mass 8.00 g so that its net charge is -3.20 × 10-9 C. (a). Find the number of excess electrons on the sphere. (b). How many excess electrons are there per lead atom? The atomic number of lead is 8
> A box is separated by a partition into two parts of equal volume. The left side of the box contains 500 molecules of nitrogen gas; the right side contains 100 molecules of oxygen gas. The two gases are at the same temperature. The partition is punctured,
> Two moles of an ideal gas occupy a volume V. The gas expands isothermally and reversibly to a volume 3V. (a). Is the velocity distribution changed by the isothermal expansion? Explain. (b). Use Eq. (20.23) to calculate the change in entropy of the gas.
> Premium gasoline produces 1.23 × 108 J of heat per gallon when it is burned at approximately 400°C (although the amount can vary with the fuel mixture). If a car’s engine is 25% efficient, three-fourths of that heat is expelled into the air, typically at
> A proton is placed in a uniform electric field and then released. Then an electron is placed at this same point and released. Do these two particles experience the same force? The same acceleration? Do they move in the same direction when released?
> (a). Calculate the change in entropy when 1.00 kg of water at 1000C is vaporized and converted to steam at 1000C. (b). Compare your answer to the change in entropy when 1.00 kg of ice is melted at 00C, calculated in Example 20.5 (Section 20.7). Is the c
> What is the change in entropy of 0.130 kg of helium gas at the normal boiling point of helium when it all condenses isothermally to 1.00 L of liquid helium? (Hint: See Table 17.4 in Section 17.6.) Table 17.4: Normal Melting Point Normal Boiling Poi
> Three moles of an ideal gas undergo a reversible isothermal compression at 20.00C. During this compression, 1850 J of work is done on the gas. What is the change of entropy of the gas?
> You make tea with 0.250 kg of 85.00C water and let it cool to room temperature (20.00C). (a). Calculate the entropy change of the water while it cools. (b). The cooling process is essentially isothermal for the air in your kitchen. Calculate the change
> A 15.0-kg block of ice at 0.00C melts to liquid water at 0.00C inside a large room at 20.00C. Treat the ice and the room as an isolated system, and assume that the room is large enough for its temperature change to be ignored. (a). Is the melting of the
> You decide to take a nice hot bath but discover that your thoughtless roommate has used up most of the hot water. You fill the tub with 195 kg of 30.00C water and attempt to warm it further by pouring in 5.00 kg of boiling water from the stove. (a). Is t
> A 4.50-kg block of ice at 0.00°C falls into the ocean and melts. The average temperature of the ocean is 3.50°C, including all the deep water. By how much does the change of this ice to water at 3.50°C alter the entropy of the world? Does the entropy inc
> A Carnot refrigerator is operated between two heat reservoirs at temperatures of 320 K and 270 K. (a). If in each cycle the refrigerator receives 415 J of heat energy from the reservoir at 270 K, how many joules of heat energy does it deliver to the res
> A certain brand of freezer is advertised to use 730 kW ∙ h of energy per year. (a). Assuming the freezer operates for 5 hours each day, how much power does it require while operating? (b). If the freezer keeps its interior at -5.00C in a 20.00C room, w
> A Carnot engine has an efficiency of 66% and performs 2.5 × 104 J of work in each cycle. (a). How much heat does the engine extract from its heat source in each cycle? (b). Suppose the engine exhausts heat at room temperature (20.00C). What is the temp
> (a).In a certain region of space, the volume charge density
> An ice-making machine operates in a Carnot cycle. It takes heat from water at 0.00C and rejects heat to a room at 24.00C. Suppose that 85.0 kg of water at 0.00C are converted to ice at 0.00C. (a). How much heat is discharged into the room? (b). How muc
> A refrigerator has a coefficient of performance of 2.25, runs on an input of 135 W of electrical power, and keeps its inside compartment at 5°C. If you put a dozen 1.0-L plastic bottles of water at 31°C into this refrigerator, how long will it take for t
> A freezer has a coefficient of performance of 2.40. The freezer is to convert 1.80 kg of water at 25.00C to 1.80 kg of ice at -5.00C in one hour. (a). What amount of heat must be removed from the water at 25.00C to convert it to ice at -5.00C? (b). How
> A refrigerator has a coefficient of performance of 2.10. In each cycle it absorbs 3.10 × 104 J of heat from the cold reservoir. (a). How much mechanical energy is required each cycle to operate the refrigerator? (b). During each cycle, how much heat is
> The coefficient of performance K = H/P is a dimensionless quantity. Its value is independent of the units used for H and P, as long as the same units, such as watts, are used for both quantities. However, it is common practice to express H in Btu/h and P
> The Otto-cycle engine in a Mercedes-Benz SLK230 has a compression ratio of 8.8. (a). What is the ideal efficiency of the engine? Use γ = 1.40. (b). The engine in a Dodge Viper GT2 has a slightly higher compression ratio of 9.6. How much increase in the
> (a). Calculate the theoretical efficiency for an Otto-cycle engine with γ = 1.40 and r = 9.50. (b). If this engine takes in 10,000 J of heat from burning its fuel, how much heat does it discard to the outside air?
> A solid conducting sphere with radius R that carries positive charge Q is concentric with a very thin insulating shell of radius 2R that also carries charge Q. The charge Q is distributed uniformly over the insulating shell. (a). Find the electric field
> A solid conducting sphere carrying charge q has radius a. It is inside a concentric hollow conducting sphere with inner radius b and outer radius c. The hollow sphere has no net charge. (a). Derive expressions for the electric field magnitude in terms o
> A very long, solid cylinder with radius R has positive charge uniformly distributed throughout it, with charge per unit volume
> When two point charges of equal mass and charge are released on a frictionless table, each has an initial acceleration (magnitude) a0. If instead you keep one fixed and release the other one, what will be its initial acceleration: a0, 2a0, or a0/2? Expla
> A very long conducting tube (hollow cylinder) has inner radius a and outer radius b. It carries charge per unit length +
> A long coaxial cable consists of an inner cylindrical conductor with radius a and an outer coaxial cylinder with inner radius b and outer radius c. The outer cylinder is mounted on insulating supports and has no net charge. The inner cylinder has a unifo
> A long line carrying a uniform linear charge density +50.0 µC/m runs parallel to and 10.0 cm from the surface of a large, flat plastic sheet that has a uniform surface charge density of -100 µC/m2 on one side. Find the location of all points where an a p
> The electric field
> Two particles having charges q1 = 0.500 nC and q2 = 8.00 nC are separated by a distance of 1.20 m. At what point along the line connecting the two charges is the total electric field due to the two charges equal to zero?
> Point charge q1 = -6.00 × 10-6 C is on the x-axis at x = -0.200 m. Point charge q2 is on the x-axis at x = +0.400 m. Point charge q3 = +3.00 × 10-6 C is at the origin. What is q2 (magnitude and sign) (a). if the net force on q3 is 6.00 N in the +x-direc
