University Physics 13th Edition solutions

University Physics 13
Problem 1DQ 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.

University Physics 13
Problem 1E A flat sheet of paper of area 0.250 m2 is oriented so that the normal to the sheet is at an angle of 60o 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) depend on the shape of the sheet? W

University Physics 13
Problem 2DQ Suppose that in Fig. 22.15 both charges were positive. What would be the fluxes through each of the four surfaces in the example?

University Physics 13
Problem 2E A 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 75.0 N/C that is directed at 20 from the plane of the sheet (Fig.). Find the magnitude of the electric flux th

University Physics 13
Problem 3DQ 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?

University Physics 13
Problem 3E You measure an electric field of 1.25 X 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 this

University Physics 13
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?

University Physics 13
Problem 4E It was shown in Example 21.11 (Section 21.5) that the electric field due to an infinite line of charge is perpendicular to the

University Physics 13
Problem 5DQ 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

University Physics 13
Problem 5E A hemispherical surface with radius r in a region of uniform electric field has its axis aligned parallel to the direction of the field. Calculate the flux through the surface.

University Physics 13
Problem 6DQ 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 isnt this possible?

University Physics 13
Problem 6E The cube in ?Fig. E22.6 has sides of length L = 10.0 cm. The electric field is uniform, has magnitude E = 4.00 X 103 N/C, and is parallel to the xy-plane at an angle of 53.1o measured from the +x-axis toward the +y-axis. (a) What is the electric flux through e

University Physics 13
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 sphere. Is all the net charge on the sphere sti

University Physics 13
Problem 7E BIO 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 t

University Physics 13
Problem 8DQ If the electric field of a point charge were proportional to 1/r3 instead of 1/r2, would Gausss law still be valid? Explain your reasoning. (?Hint: Consider a spherical Gaussian surface centered on a single point charge.)

University Physics 13
Problem 8E 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: (a) S1; (b) S2; (c) S3; (d) S4; (e) S5. (f

University Physics 13
Problem 9DQ 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?

University Physics 13
Problem 9E 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 35.0 ???C. Find the electric field (a) just inside the paint layer; (b) just outside the paint layer; (c) 5.00 cm outside

University Physics 13
Problem 10DQ 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 flux th

University Physics 13
Problem 10E 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 and

University Physics 13
Problem 11DQ 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 tha

University Physics 13
Problem 11E A 6.20-C 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.

University Physics 13
Problem 12DQ A solid conductor has a cavity in its interior. Would the presence of a point charge inside the cavity affect the electric field outside the conductor? Why or why not? Would the presence of a point charge outside the conductor affect the electric field insid

University Physics 13
Problem 12E Electric Fields in an Atom. 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 X 10-15 m. (a) What is the electric field this nucle

University Physics 13
Problem 13DQ Explain this statement: In a static situation, the electric field at the surface of a conductor can have no component parallel to the surface because this would violate the condition that the charges on the surface are at rest. Would this statement be valid

University Physics 13
Problem 13E A point charge of +5.00 ???C is located on the ?x?-axis at ?x = 4.00 m, next to a spherical surface of radius 3.00 m centered of the origin. (a) Calculate the magnitude of the electric field at ?x = 3.00 m. (b) Calculate the magnitude of the electric held

University Physics 13
Problem 14DQ In a certain region of space, the electric field is uniform. (a) Use Gausss law to prove that this region of space must be electrically neutral; that is, the volume charge density ? must be zero. (b) Is the converse true? That is, in a region of space where there

University Physics 13
Problem 14E 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.

University Physics 13
Problem 15DQ (a) In a certain region of space, the volume charge density ? has a uniform positive value. Can be uniform in this region? Explain. (b) Suppose that in this region of uniform positive ? there is a bubble within which ? = 0. Can be uniform within t

University Physics 13
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 \(\mu \mathrm{C} / \mathrm{m}\). What magnitude of force does one line of charge exert on a 0.0500-m section of the other line of charge?

University Physics 13
Poblem 16E 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 X 1016 N ? m2/C at the planets surface. Calculate: (a) the total electric charge on the planet

University Physics 13
Problem 17E How many excess electrons must be added to an isolated spherical conductor 32.0 cm in diameter to produce an electric field of 1150 N/C just outside the surface?

University Physics 13
Problem 18E 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?

University Physics 13
Problem 19E A very long uniform line of charge has charge per unit length 4.80 C/m and lies along the x-axis. A second long uniform line of charge has charge per unit length -2.40 C/m and is parallel to the x-axis at y = 0.400 m. What is the net electric field (magnitude

University Physics 13
Problem 20E (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 long

University Physics 13
Problem 21E 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 X 10-6 C/m2. A charge of -0.500 C is now introduced at the center of the cavity inside the sphere. (a) What is the new

University Physics 13
Problem 22E A point charge of 2.00 ?C is located in the center of a spherical cavity of radius 6.50 cm inside an insulating charged solid. The charge density in the solid is ?? = 7.35 104 C/m3. Calculate the electric field inside the solid at a distance of 9.50 cm f

University Physics 13
Problem 23E The electric field at a distance of 0.145 m from the sur-face of a solid insulating sphere with radius 0.355 m is 1750 N/C. (a) Assuming the spheres charge is uniformly distributed, what is the charge density inside it? (b) Calculate the electric field inside

University Physics 13
CP A very small object with mass \(8.20 \times 10^{-9}\) kg and positive charge \(6.50 \times 10^{-9}\) C is projected directly toward a very large insulating sheet of positive charge that has uniform surface charge density \(5.90 \times 10^{-8} \mathrm{C} / \mathrm{m}^{2}\). The object is initially

University Physics 13
Problem 25E CP At time t = 0 a proton is a distance of 0.360 m from a very large insulating sheet of charge and is moving parallel to the sheet with speed 9.70 X 102 m/s. The sheet has uniform surface charge density 2.34 X 10-9 C/m2. What is the speed of the proton at t

University Physics 13
Problem 26E CP 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 X 10-12 C/m2. (a) How much work is done on the electron by the electric field of the sheet as the electron move

University Physics 13
Problem 27E An insulating sphere of radius R = 0.160 m has uniform charge density ?? = +7.20 10?9 C/m3. A small object that can be treated as a point charge is released from rest just outside the surface of the sphere. The small object has positive charge ?q = 3.40 106

University Physics 13
Problem 28E A conductor with an inner cavity, like that shown in Fig.

University Physics 13
Problem 29E Apply Gausss law to the Gaussian surfaces and

University Physics 13
Problem 30E A square insulating sheet 80.0 cm on a side is held horizontally. The sheet has 7.50 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 point 10

University Physics 13
Problem 31E An infinitely long cylindrical conductor has radius? ?and same as if all the charge were on the axis. Compare your result to the result for a line of charge in Example 22.6 (Section 22.4).

University Physics 13
Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities \(\sigma_{1}\), \(\sigma_{2}\), \(\sigma_{3}\), and \(\sigma_{4}\) on their surfaces (?Fig. E22.30 ). These surface charge densities have the values \(\sigma_{1}\) = \(-6.00 \mu \mathrm{C} / \mathrm{m}^{2

University Physics 13
Problem 33E A negative charge ?Q is placed inside the cavity of a hollow metal solid. The outside or the solid is grounded by connecting a conducting wire between it and the earth. (a) Is there any excess charge induced on the inner surface of the piece of metal? If

University Physics 13
Problem 34P A cube has sides of length ?L ?= 0.300 m. It is placed with one corner at the origin as shown in Fig. E22.6. The electric

University Physics 13
Problem 35P The electric field in ?Fig. P22.35 is everywhere parallel to the x -axis, so the components Ey and Ez are zero. The x -component of the field Ex depends on x but not on y or z. At points in the yz-plane (where x = 0), Ex = 125 N/C. (a) What is the e

University Physics 13
Problem 36P CALC In a region of space there is an electric field that is in the z-direction and that has magnitude E = [964 N/(C ? m)]x . Find the flux for this field through a square in the xy-plane at z = 0 and with side length 0.350 m. One side of the square

University Physics 13
Problem 37P The electric field at one face of a parallelepiped is uniform over the entire face and is directed out of the face. At the opposite face, the electric field is also uniform over the entire face and is directed into that face (?Fig. P22.37?). The

University Physics 13
Problem 38P A long line carrying a uniform linear charge density +50.0 C/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 C/m2 on one side. Find the location of all points where an ? particle

University Physics 13
Problem 39P The Coaxial Cable. 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 cy

University Physics 13
Problem 40P A very long conducting tube (hollow cylinder) has inner radius a and outer radius b. It carries charge per unit length +?, where a is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge pe

University Physics 13
Problem 41P Repeat Problem, but now let the conducting tube have charge per unit length ? ??. As in the line of charge has charge per unit length +? ??.

University Physics 13
Problem 42P A very long, solid cylinder with radius R has positive charge uniformly distributed throughout it, with charge per unit volume ?. (a) Derive the expression for the electric field inside the volume at a distance r from the axis of the cylinder in terms of

University Physics 13
Problem 43P CP A small sphere with mass 4.00 X 10-6 kg and charge 5.00 X 10-8 C hangs from a thread near a very large, charged insulating sheet (?Fig. P22.33?). The charge density on the surface of the sheet is uniform and equal to -2.50 X 10-9 C/m2. Find the angle o

University Physics 13
Problem 44P A Sphere in a Sphere. 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 m

University Physics 13
Problem 45P 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 (m

University Physics 13
Problem 46P A conducting spherical shell with inner radius a and outer radius b has a positive point charge Q located at its center. The total charge on the shell is - 3Q, and it is insulated from its surroundings (?Fig. P22.44?). (a) Derive expressions for the elect

University Physics 13
Problem 47P Concentric Spherical Shells. A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d (?Fig. P22.45?). The inner shell has total charge +2q, an

University Physics 13
Problem 48P Repeat Problem 22.45, but now let the outer shell have charge -2q. The inner shell still has charge +2q. 22.45 . ?Concentric Spherical Shells. A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducti

University Physics 13
Problem 49P Repeal Problem, but now let the outer shell have charge ?4?q?. As in Problem, the inner shell has charge +2?q?. Problem: Concentric Spherical Shells. A small conducting spherical shell with inner radius a and outer radius ?b is concentric with

University Physics 13
Problem 50P A solid conducting sphere with radius R carries a positive total charge Q . The sphere is surrounded by an insulating shell with inner radius R and outer radius 2R. The insulating shell has a uniform charge density ?. (a) Find the value of ? so that the n

University Physics 13
Problem 51P Negative charge -Q is distributed uniformly over the surface of a thin spherical insulating shell with radius R. Calculate the force (magnitude and direction) that the shell exerts on a positive point charge q located a distance (a) r > R from the center

University Physics 13
Problem 52P (a) How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere 30.0 cm in diameter to produce an electric field of magnitude 1390 N/C just outside the surface of the sphere? (b) What is the electric field at a poin

University Physics 13
CALC An insulating hollow sphere has inner radius \(a\) and outer radius \(b\). Within the insulating material the volume charge density is given by \(\rho(r)=\frac{\alpha}{r}\), where \(\alpha\) is a positive constant. (a) In terms of \(\alpha\) and \(a\), what is the magnitude of the electric fi

University Physics 13
Problem 54P CP Thomsons Model of the Atom. Early in the 20th century, a leading model of the structure of the atom was that of English physicist J. J. Thomson (the discoverer of the electron). In Thomsons model, an atom consisted of a sphere of positively charged mat

University Physics 13
Problem 55P Thomsons Model of the Atom, Continued. Using Thomsons (outdated) model of the atom described in Problem 22.50, consider an atom consisting of two electrons, each of charge -e, embedded in a sphere of charge +2e and radius R. In equilibrium, each electron is a

University Physics 13
Problem 56P A Uniformly Charged Slab. A slab of insulating material has thickness 2d and is oriented so that its faces are parallel to the yz-plane and given by the planes x = d and x = -d. The y- and z-dimensions of the slab are very large compared to d; treat them

University Physics 13
Problem 57P CALC A Nonuniformly Charged Slab. Repeat Problem 22.54, but now let the charge density of the slab be given by ?(x) = ?0(x/d)2, where ?0 is a positive constant. 22.54 . ?A Uniformly Charged Slab. A slab of insulating material has thickness 2d and

University Physics 13
Problem 58P CALC A nonuniform, but spherically symmetric, distribution of charge has a charge density ?(r) given as follows: where ?0 is a positive constant. (a) Find the total charge contained in the charge distribution. Obtain an expression for the ele

University Physics 13
Problem 59P Gausss Law for Gravitation. The gravitational force between two point masses separated by a distance ?r is proportional to 1/?r?2, just like the electric force between two point charges. Because of this similarity between gravitational and electric inter

University Physics 13
Problem 60P Applying Gausss Law for Gravitation. ?Using Gausss law for gravitation (derived in part (b) of Problem 22.59), show that the following statements are true: (a) For any spherically symmetric mass distribution with total mass ?M?, the acceleration due to gravity outsid

University Physics 13
Problem 61P (a) An insulating sphere with radius a has a uniform charge density ?. The sphere is not centered at the origin but at Show that the electric field inside the sphere is given by (b) An insulating sphere of r

University Physics 13
Problem 62P A very long, solid insulating cylinder has radius R; bored along its entire length is a cylindrical hole with radius a. The axis of the hole is a distance b from the axis of the cylinder, where a < b < R (?Fig. P22.58?). The solid material of the cylinder has

University Physics 13
Problem 63P Positive charge ?Q is distributed uniformly over each of two spherical volumes with radius ?R?. One sphere of charge is centered at the origin and the other at ?x = 2?R (Fig). Find the magnitude and direction of the net electric field due to these two dis

University Physics 13
Problem 64P Repeat Problem, but now let the left-hand sphere have positive charge ?Q and let the right-hand sphere have negative charge ??Q?. Problem: Positive charge ?Q is distributed uniformly over each of two spherical volumes with radius ?R?. One spher

University Physics 13
Problem 65P CALC A nonuniform, but spherically symmetric, distribution of charge has a charge density ?(r) given as follows: where ?0 = 3Q/?R3 is a positive constant. (a) Show that the total charge contained in the charge distribution is Q. (b) Show that

University Physics 13
Problem 66CP A region in space contains a total positive charge ?Q that is distributed spherically such that the volume charge density ? ?? ?r?) is given by Here ? is a positive constant having units of C/m3. (a) Determine ? in terms of ?Q and ?R?. (b) Usi

University Physics 13
CP CALC A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density \(\rho(r)\) is given by \(\rho(r)=3 \alpha r /(2 R) \quad\) for \(r \leq R / 2\) \(\rho(r)=\alpha\left[1-(r / R)^2\right] \quad\)