A hemispherical surface with radius r in a region of uniform electric field
> 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?
> A student asked, “Since electrical potential is always proportional to potential energy, why bother with the concept of potential at all?” How would you respond?
> 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
> 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
> 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.
> 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
