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Physics for Scientists and Engineers A Strategic Approach with Modern Physics 4th edition Randall D. Knight - Solutions

A 5.0-cm-diameter metal ball has a surface charge density of 10 μC/m2. How much work is required to remove one electron from this ball?
The two halves of the rod in FIGURE EX25.35 are uniformly charged to ±Q. What is the electric potential at the point indicated by the dot? ++++++++ FIGURE EX25.35
Two point charges qaand qbare located on the x-axis at x = a and x = b. FIGURE EX25.34 is a graph of V, the electric potential. a. What are the signs of qa and qb?b. What is the ratio |qa/qb|?c. Draw a graph of Ex, the x-component of the electric field, as a function of x. + a b FIGURE EX25.34
A -2.0 nC charge and a +2.0 nC charge are located on the x-axis at x = -1.0 cm and x = +1.0 cm, respectively.a. Other than at infinity, is there a position or positions on the x-axis where the electric field is zero? If so, where?b. Other than at infinity, at what position or positions on the
The electric potential at the dot in FIGURE EX25.32 is 3140 V.What is charge q? -5.0 nC 2.0 cm 4.0 cmi 5.0 nC FIGURE EX25.32
What is the electric potential at the point indicated with the dot in FIGURE EX25.31? 1.0 nC 3.0 cm,' 3.0 cm 3.0 cm -2.0 nC -2.0 nC FIGURE EX25.31
What is the electric potential at the point indicated with the dot in FIGURE EX25.30? 2.0 nC -1.0 nC 3.0 cm 14.0 cm +, 2.0 nC FIGURE EX25.30
In a semiclassical model of the hydrogen atom, the electron orbits the proton at a distance of 0.053 nm.a. What is the electric potential of the proton at the position of the electron?b. What is the electron’s potential energy?
A 1.0-mm-diameter ball bearing has 2.0 × 109 excess electrons.What is the ball bearing’s potential?
a. What is the electric potential at points A, B, and C in FIGURE EX25.27?b. What are the potential differences Î”VAB= VB- VAand Î”VCB= VB- VC? 2,0 cm, 1.0 cm в +, 2.0 nC
In FIGURE EX25.26, a proton is fired with a speed of 200,000 m/s from the midpoint of the capacitor toward the positive plate. a. Show that this is insufficient speed to reach the positive plate.b. What is the proton??s speed as it collides with the negative plate? OV 500 V 200,000 m/s + FIGURE
Two 2.0-cm-diameter disks spaced 2.0 mm apart form a parallel-plate capacitor. The electric field between the disks is 5.0 × 105 V/m.a. What is the voltage across the capacitor?b. An electron is launched from the negative plate. It strikes the positive plate at a speed of 2.0 × 107 m/s. What was
Two 2.00 cm × 2.00 cm plates that form a parallel-plate capacitor are charged to ±0.708 nC. What are the electric field strength inside and the potential difference across the capacitor if the spacing between the plates is(a) 1.00 mm(b) 2.00 mm?
A 3.0-cm-diameter parallel-plate capacitor has a 2.0 mm spacing. The electric field strength inside the capacitor is 1.0 × 105 V/m.a. What is the potential difference across the capacitor?b. How much charge is on each plate?
a. What is the potential of an ordinary AA or AAA battery?b. An AA battery is connected to a parallel-plate capacitor having 4.0 cm × 4.0 cm plates spaced 1.0 mm apart. How much charge does the battery supply to each plate?
Show that 1 V/m = 1 N/C.
Physicists often use a different unit of energy, the electron volt, when dealing with energies at the atomic level. One electron volt, abbreviated eV, is defined as the amount of kinetic energy gained by an electron upon accelerating through a 1.0 V potential difference.a. What is 1.0 electron volt
A student wants to make a very small particle accelerator using a 9.0 V battery. What speed will(a) A proton(b) An electron have after being accelerated from rest through the 9.0 V potential difference?
In proton-beam therapy, a high-energy beam of protons is fired at a tumor. As the protons stop in the tumor, their kinetic energy breaks apart the tumor’s DNA, thus killing the tumor cells. For one patient, it is desired to deposit 0.10 J of proton energy in the tumor. To create the proton beam,
Through what potential difference must a proton be accelerated to reach the speed it would have by falling 100 m in vacuum?
An electron with an initial speed of 500,000 m/s is brought to rest by an electric field.a. Did the electron move into a region of higher potential or lower potential?b. What was the potential difference that stopped the electron?
A proton with an initial speed of 800,000 m/s is brought to rest by an electric field.a. Did the proton move into a region of higher potential or lower potential?b. What was the potential difference that stopped the proton?
What potential difference is needed to accelerate a He+ ion (charge +e, mass 4 u) from rest to a speed of 2.0 × 106 m/s?
What potential difference is needed to accelerate an electron from rest to a speed of 2.0 × 106 m/s?
What is the speed of an electron that has been accelerated from rest through a potential difference of 1000 V?
Reproduce FIGURE Q25.12 on your paper. Then draw a dot (or dots) on the figure to show the position (or positions) at which the electric potential is zero. | FIGURE Q25.12
What is the speed of a proton that has been accelerated from rest through a potential difference of -1000 V?
FIGURE Q25.11 shows three points near two point charges. The charges have equal magnitudes. For each part, rank in order, from most positive to most negative, the potentials Vato Vc.a.b. +, +) b a +, a
FIGURE EX25.10 shows the potential energy of an electric dipole. Consider a dipole that oscillates between ?60?. a. What is the dipole??s mechanical energy?b. What is the dipole??s kinetic energy when it is aligned with the electric field? U (µJ) 2- -180° 0° 180° FIGURE EX25.10
FIGURE Q25.10 shows two points near a positive point charge.a. What is the ratio V2/V1of the electric potentials? Explain.b. What is the ratio E2/E1of the electric field strengths? 1 mm 2 3 mm FIGUREQ25.10
A water molecule perpendicular to an electric field has 1.0 × 10-21 J more potential energy than a water molecule aligned with the field. The dipole moment of a water molecule is 6.2 × 10-30 C m. What is the strength of the electric field?
FIGURE Q25.9 shows two points inside a capacitor. Let V = 0 V at the negative plate.a. What is the ratio V2/V1of the electric potentials? Explain.b. What is the ratio E2/E1of the electric field strengths? 1 mm 2 3 mm FIGURE Q25.9
Two positive point charges are 5.0 cm apart. If the electric potential energy is 72 μJ, what is the magnitude of the force between the two charges?
Rank in order, from largest to smallest, the electric potentials Vato Veat points a to e in FIGURE Q25.8. Explain. a • b. + ++ + + + + + + + + + + +++ FIGURE Q25.8
What is the electric potential energy of the group of charges in FIGURE EX25.7? -4.0 nC 3.0 nC + 3.0 cm 14.0 cm 3.0 nC FIGURE EX25.7
A capacitor with plates separated by distance d is charged to a potential difference ΔVC. All wires and batteries are disconnected, then the two plates are pulled apart (with insulated handles) to a new separation of distance 2d.a. Does the capacitor charge Q change as the separation increases? If
What is the electric potential energy of the group of charges in FIGURE EX25.6? 1.0 nC 3.0 cm \ 3.0 cm 3.0 сm -2.0 nC -2.0 nC FIGURE EX25.6 +
FIGURE Q25.6 shows the electric potential along the x-axis. a. Draw a graph of the potential energy of a 0.1 C charged particle. Provide a numerical scale for both axes.b. If the charged particle is shot toward the right from x = 1 m with 1.0 J of kinetic energy, where is its turning point? Use
What is the potential energy of the electron-proton interactions in FIGURE EX25.5? The electrons are fixed and cannot move. Proton 0.50 nm Electrons - 2.0 nm 0.50 nm FIGURE EX25.5
Rank in order, from most positive to most negative, the potential energies Uato Ufof the six electric dipoles in the uniform electric field of FIGURE Q25.5. Explain. a d. e
A proton is released from rest at the positive plate of a parallelplate capacitor. It crosses the capacitor and reaches the negative plate with a speed of 50,000 m/s. The experiment is repeated with a He+ ion (charge e, mass 4 u). What is the ion’s speed at the negative plate?
Two protons are launched with the same speed from point 1 inside the parallel-plate capacitor of FIGURE Q25.4. Points 2 and 3 are the same distance from the negative plate. a. Is ΔU1??2, the change in potential energy along the path 1 ???2, larger than, smaller than, or equal to ΔU1??3?b. Is the
A proton is released from rest at the positive plate of a parallelplate capacitor. It crosses the capacitor and reaches the negative plate with a speed of 50,000 m/s. What will be the final speed of an electron released from rest at the negative plate?
An electron moves along the trajectory of FIGURE Q25.3 from i to f. a. Does the electric potential energy increase, decrease, or stay the same? Explain.b. Is the electron??s speed at f greater than, less than, or equal to its speed at i? Explain. i FIGURE Q25.3
The electric field strength is 50,000 N/C inside a parallel plate capacitor with a 2.0 mm spacing. A proton is released from rest at the positive plate. What is the proton’s speed when it reaches the negative plate?
FIGURE Q25.2 shows the potential energy of a proton (q = +e) and a lead nucleus (q = +82e). The horizontal scale is in units of femtometers, where 1 fm = 10-15m. a. A proton is fired toward a lead nucleus from very far away.How much initial kinetic energy does the proton need to reach a turning
The electric field strength is 20,000 N/C inside a parallel plate capacitor with a 1.0 mm spacing. An electron is released from rest at the negative plate. What is the electron’s speed when it reaches the positive plate?
a. Charge q1 is distance r from a positive point charge Q. Charge q2 = q1/3 is distance 2r from Q. What is the ratio U1/U2 of their potential energies due to their interactions with Q?b. Charge q1 is distance s from the negative plate of a parallel-plate capacitor. Charge q2 = q1/3 is distance 2s
A spherical ball of charge has radius R and total charge Q. The electric field strength inside the ball (r ≤ R) is E(r) = r4Emax/R4.a. What is Emax in terms of Q and R?b. Find an expression for the volume charge density ρ(r) inside the ball as a function of r.c. Verify that your charge density
sphere of radius R has total charge Q. The volume charge density (C/m3) within the sphere isThis charge density decreases linearly from Ï0 at the center to zero at the edge of the sphere.a. Show that Ï0 = 3Q/Ï€R3.b. Show that the electric field inside the sphere
A sphere of radius R has total charge Q. The volume charge density (C/m3) within the sphere is ρ(r) = C/r2, where C is a constant to be determined.a. The charge within a small volume dV is dq = ρ dV. The integral of ρ dV over the entire volume of the sphere is the total charge Q. Use this fact
An infinite cylinder of radius R has a linear charge density λ.The volume charge density (C/m3) within the cylinder (r ≤ R) is ρ(r) = rρ0/R, where ρ0 is a constant to be determined.a. Draw a graph of ρ versus x for an x-axis that crosses the cylinder perpendicular to the cylinder axis. Let x
All examples of Gauss€™s law have used highly symmetric surfaces where the flux integral is either zero or EA. Yet we€™ve claimed that the net Î¦e= Qin/Ñ”0is independent of the surface.This is worth checking. FIGURE CP24.57 shows a cube of edge length L
Newton’s law of gravity and Coulomb’s law are both inverse square laws. Consequently, there should be a “Gauss’s law for gravity.”a. The electric field was defined as E = F on q/q, and we used this to find the electric field of a point charge. Using analogous reasoning, what is the
An early model of the atom, proposed by Rutherford after his discovery of the atomic nucleus, had a positive point charge +Ze (the nucleus) at the center of a sphere of radius R with uniformly distributed negative charge -Ze. Z is the atomic number, the number of protons in the nucleus and the
A spherical shell has inner radius Rin and outer radius Rout. The shell contains total charge Q, uniformly distributed. The interior of the shell is empty of charge and matter.a. Find the electric field strength outside the shell, r ≥ Rout.b. Find the electric field strength in the interior of
A long cylinder with radius b and volume charge density ρ has a spherical hole with radius a < b centered on the axis of the cylinder. What is the electric field strength inside the hole at radial distance r < a in a plane that is perpendicular to the cylinder through the center of the hole?
The electric field must be zero inside a conductor in electrostatic equilibrium, but not inside an insulator. It turns out that we can still apply Gauss’s law to a Gaussian surface that is entirely within an insulator by replacing the right-hand side of Gauss’s law, Qin/є0, with Qin/є, where
The electric field must be zero inside a conductor in electrostatic equilibrium, but not inside an insulator. It turns out that we can still apply Gauss’s law to a Gaussian surface that is entirely within an insulator by replacing the right-hand side of Gauss’s law, Qin/є0, with Qin/є, where
A very long, uniformly charged cylinder has radius R and linear charge density λ. Find the cylinder’s electric field strength(a) Outside the cylinder, r ≥ R,(b) Inside the cylinder, r ≤ R.(c) Show that your answers to parts a and b match at the boundary, r = R.
A long, thin straight wire with linear charge density λ runs down the center of a thin, hollow metal cylinder of radius R.The cylinder has a net linear charge density 2λ. Assume λ is positive. Find expressions for the electric field strength(a) Inside the cylinder, r < R,(b) Outside the
FIGURE P24.48 shows two very large slabs of metal that are parallel and distance l apart. The top and bottom of each slab has surface area A. The thickness of each slab is so small in comparison to its lateral dimensions that the surface area around the sides is negligible. Metal 1 has total charge
FIGURE P24.47 shows an infinitely wide conductor parallel to and distance d from an infinitely wide plane of charge with surface charge density Î·. What are the electric fields E1to E4in regions 1 to 4? Conductor 3 Surface charge density n 4 FIGURE P24.47 2.
An infinite slab of charge of thickness 2z0 lies in the xy plane between z = -z0 and z = +z0. The volume charge density ρ (C/m3) is a constant.a. Use Gauss’s law to find an expression for the electric field strength inside the slab (-z0 ≤ z ≤ z0).b. Find an expression for the electric field
The three parallel planes of charge shown in FIGURE P24.45 have surface charge densities -1/2Î·, Î·, and -1/2Î·. Find the electric fields E1to E4in regions 1 to 4. 7++++++++++++++++++ 3 FIGURE P24.45 4
A uniformly charged ball of radius a and charge -Q is at the center of a hollow metal shell with inner radius b and outer radius c. The hollow sphere has net charge +2Q. Determine the electric field strength in the four regions r ≤ a, a < r < b, b ≤ r ≤ c, and r > c.
Part A Find the electric field inside a hollow plastic ball of radius R that has charge Q uniformly distributed on its outer surface. Give your answer as a multiple of Q/ε0. Part B Find the electric field outside this ball. Give your answer as a multiple of Q/ε0. Express your answer in terms of
A positive point charge q sits at the center of a hollow spherical shell. The shell, with radius R and negligible thickness, has net charge -2q. Find an expression for the electric field strength(a) Inside the sphere, r < R,(b) Outside the sphere, r > R. In what direction does the electric
A hollow metal sphere has 6 cm and 10 cm inner and outer radii, respectively. The surface charge density on the inside surface is -100 nC/m2. The surface charge density on the exterior surface is +100 nC/m2. What are the strength and direction of the electric field at points 4, 8, and 12 cm from
Figure 24.32b showed a conducting box inside a parallel plate capacitor. The electric field inside the box is E = 0. Suppose the surface charge on the exterior of the box could be frozen. Draw a picture of the electric field inside the box after the box, with its frozen charge, is removed from the
The earth has a vertical electric field at the surface, pointing down, that averages 100 N/C. This field is maintained by various atmospheric processes, including lightning. What is the excess charge on the surface of the earth?
FIGURE P24.38 shows a solid metal sphere at the center of a hollow metal sphere. What is the total charge on (a) The exterior of the inner sphere,(b) The inside surface of the hollow sphere,(c) The exterior surface of the hollow sphere? Conducting spheres 5 ст 15,000 N/C | 15,000 N/C 10 cm E E 15
A 20-cm-radius ball is uniformly charged to 80 nC.a. What is the ball’s volume charge density (C/m3)?b. How much charge is enclosed by spheres of radii 5, 10, and 20 cm?c. What is the electric field strength at points 5, 10, and 20 cm from the center?
A hollow metal sphere has inner radius a and outer radius b.The hollow sphere has charge + 2Q. A point charge + Q sits at thecenter of the hollow sphere.a. Determine the electric fields in the three regions r ≤ a,a < r < b, and r ≥ b.b. How much charge is on the inside surface of the
A neutral conductor contains a hollow cavity in which there is a +100 nC point charge. A charged rod then transfers -50 nC to the conductor. Afterward, what is the charge(a) On the inner wall of the cavity,(b) On the exterior surface of the conductor?
A spherically symmetric charge distribution produces the electric field E = (5000r2)r̂ N/C, where r is in m.a. What is the electric field strength at r = 20 cm?b. What is the electric flux through a 40-cm-diameter spherical surface that is concentric with the charge distribution?c. How much charge
A 10 nC charge is at the center of a 2.0 m × 2.0 m × 2.0 m cube. What is the electric flux through the top surface of the cube?
Charges q1 = -4Q and q2 = +2Q are located at x = -a and x = +a, respectively. What is the net electric flux through a sphere of radius 2a centered(a) At the origin(b) At x = 2a?
A tetrahedron has an equilateral triangle base with 20-cm long edges and three equilateral triangle sides. The base is parallel to the ground, and a vertical uniform electric field of strength 200 N/C passes upward through the tetrahedron.a. What is the electric flux through the base?b. What is the
FIGURE P24.30 shows four sides of a 3.0 cm Ã— 3.0 cm Ã— 3.0 cm cube.a. What are the electric fluxes Î¦1 to Î¦4 through sides 1 to 4?b. What is the net flux through these four sides? Top view of a 3.0 cm X 3.0 cm X 3.0 cm cube 30° 500 N/C FIGURE
Find the electric fluxes Î¦1to Î¦5through surfaces 1 to 5 in FIGURE P24.29. 4.0 m 400 N/C 2.0 m 4. (2 30° FIGURE P24.29
A thin, horizontal, 10-cm-diameter copper plate is charged to 3.5 nC. If the electrons are uniformly distributed on the surface, what are the strength and direction of the electric fielda. 0.1 mm above the center of the top surface of the plate?b. At the plate’s center of mass?c. 0.1 mm below the
FIGURE EX24.27 shows a hollow cavity within a neutral conductor.A point charge Q is inside the cavity. What is the net electric flux through the closed surface that surrounds the conductor? Closed surface FIGURE EX24.27 +)
The conducting box in FIGURE EX24.26 has been given an excess negative charge. The surface density of excess electrons at the center of the top surface is 5.0 Ã— 1010 electrons/m2. What are the electric field strengths E1to E3at points 1 to 3? 1. 3 FIGURE EX24.26
The electric field strength just above one face of a copper penny is 2000 N/C. What is the surface charge density on this face of the penny?
A spark occurs at the tip of a metal needle if the electric field strength exceeds 3.0 × 106 N/C, the field strength at which air breaks down. What is the minimum surface charge density for producing a spark?
55.3 million excess electrons are inside a closed surface. What is the net electric flux through the surface?
The net electric flux through an octahedron is -1000 N m2/C. How much charge is enclosed within the octahedron?
What is the net electric flux through the cylinder of FIGURE EX24.21? +. FIGURE EX24.21 +100 nC +1 nC (inside) -100 nC
What is the net electric flux through the torus (i.e., doughnut shape) of FIGURE EX24.20? +) -1 nC (inside) +100 nC FIGURE EX24.20
FIGURE EX24.19 shows three Gaussian surfaces and the electric flux through each. What are the three charges q1, q2, and q3? Pc =-2gle, = -qle, Ф 92 Фв 3 Зд/eo 93 FIGURE EX24.19
FIGURE EX24.18 shows three charges. Draw these charges on your paper four times. Then draw two-dimensional cross sections of three-dimensional closed surfaces through which the electric flux is (a) -q/є0, (b) q/є0, (c) 3q/є0, (d) 4q/є0. +) 24 +) 29 FIGURE EX24.18
FIGURE EX24.17 shows three charges. Draw these charges on your paper four times. Then draw two-dimensional cross sections of three-dimensional closed surfaces through which the electric flux is (a) 2q/є0, (b) q/є0, (c) 0, (d) 5q/є0. -29 24 39 FIGURE EX24.17 +)
What is the net electric flux through the two cylinders shown in FIGURE EX24.16? Give your answer in terms of R and E.a.b. 2R 2R
A 1.0 cm × 1.0 cm × 1.0 cm box with its edges aligned with the xyz-axes is in the electric field E = (350x + 150)î N/C, where x is in meters. What is the net electric flux through the box?
A 3.0-cm-diameter circle lies in the xz-plane in a region where the electric field is E = (1500î + 1500ĵ - 1500k̂) N/C. What is the electric flux through the circle?
A 2.0 cm × 3.0 cm rectangle lies in the xz-plane. What is the magnitude of the electric flux through the rectangle ifa. E = (100î - 200k̂) N/C?b. E = (100î - 200ĵ) N/C?
A 2.0 cm × 3.0 cm rectangle lies in the xy-plane. What is the magnitude of the electric flux through the rectangle ifa. E = (100î - 200k̂) N/C?b. E = (100î- 200ĵ) N/C?
The electric flux through the surface shown in FIGURE EX24.11 is 25 N m2/C. What is the electric field strength? în 60° 10 cm X 20 cm FIGURE EX24.11
What is the electric flux through the surface shown in FIGURE EX24.10? în 200 N/C 130° 10 cm X 10 cm FIGURE EX24.10

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