Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Textbook Question
Chapter 22.3, Problem 1DE
A charge Q is placed on a hollow metal ball. We saw in Chapter 21 that the charge is all on the surface of the ball because metal is a conductor. How does the charge distribute itself on the ball? (a) Half on the inside surface and half on the outside surface. (b) Part on each surface in inverse proportion to the two radii. (c) Part on each surface but with a more complicated dependence on the radii than in answer (b). (d) All on the inside surface. (e) All on the outside surface.
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An insulating sphere of radius a is placed at the center of a spherical conductor whose inner radius is b and outer radius is c (see figure). The +Q charge is uniformly distributed throughout the insulator sphere, while the spherical shell is -Q charged. Find the electric field strength E as a function of the radial distance r,
a. inside the insulator ball (r<a)
b. in a<r<b
c. inside the spherical shell (b<r<c)
d. outside the shell (r>c)
e. How much charge on the inner surface of the spherical conductor (r= b), and how much on the outer surface of the spherical conductor (r = c)?
An infinitely long cylindrical conducting shell of outer radius r1 = 0.10 m and inner radius r2 = 0.08 m initially carries a surface charge density σ = -0.45 μC/m2. A thin wire, with linear charge density λ = 1.2 μC/m, is inserted along the shells' axis. The shell and the wire do not touch and there is no charge exchanged between them.
What is the new surface charge density, in microcoulombs per square meter, on the inner surface of the cylindrical shell? What is the new surface charge density, in microcoulombs per square meter, on the outer surface of the cylindrical shell?
Enter an expression for the magnitude of the electric field outside the cylinder (r > 0.1 m), in terms of λ, σ, r1, r, and ε0.
A nonuniform, but spherically symmetric, insulating sphere of charge has a charge density ρ(r)ρ(r) given as follows:
ρ(r)=ρ0(1−4r/3R)
for r≤R
ρ(r)=0
for r≥R
where ρ0 is a positive constant. This means that the amount of charge per unit volume varies with distance from the center of the sphere.
Hint: The charge enclosed in a given spherical shell of inner radius R1 and outer radius R2 is Qenc=∫R2R1 ρ(r)dV where dV=4πr^2dr (in other words, you have to integrate over each spherical shell of radius rr from the inner radius to the outer radius). Notice that if the charge is uniform, so that ρρ is a constant, and you have a solid sphere with inner radius zero and outer radius R (i.e. a normal sphere) you can pull ρρ out of the integral and it reduces to the simple expression Qenc=ρ4/3πR^3. For a non-uniformly charged sphere, however, as in this problem, you have to use the full integral to find the charge enclosed in a given region.
A) Obtain an expression for the electric field…
Chapter 22 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 22.1 - Which of the following would cause a change in the...Ch. 22.2 - A point charge Q is at the center of a spherical...Ch. 22.2 - Three 2.95 C charges are in a small box. What is...Ch. 22.3 - A charge Q is placed on a hollow metal ball. We...Ch. 22.3 - CHAPTER-OPENING QUESTIONGuess now! A nonconducting...Ch. 22.3 - Which of the following statements about Gausss law...Ch. 22 - If the electric flux through a closed surface is...Ch. 22 - Is the electric field E in Gausss law....Ch. 22 - A point charge is surrounded by a spherical...Ch. 22 - What can you say about the flux through a closed...
Ch. 22 - The electric field E is zero at all points on a...Ch. 22 - Define gravitational flux in analogy to electric...Ch. 22 - Would Gausss law be helpful in determining the...Ch. 22 - A spherical basketball (a nonconductor) is given a...Ch. 22 - In Example 226, it may seem that the electric...Ch. 22 - Suppose the line of charge in Example 226 extended...Ch. 22 - A point charge Q is surrounded by a spherical...Ch. 22 - A solid conductor carries a net positive charge Q....Ch. 22 - A point charge q is placed at the center of the...Ch. 22 - A small charged ball is inserted into a balloon....Ch. 22 - (I) A uniform electric field of magnitude 5.8 102...Ch. 22 - (I) The Earth possesses an electric field of...Ch. 22 - (II) A cube of side l is placed in a uniform field...Ch. 22 - (II) A uniform field E is parallel to the axis of...Ch. 22 - (I) The total electric flux from a cubical box...Ch. 22 - (I) Figure 2226 shows five closed surfaces that...Ch. 22 - (II) In Fig. 2227, two objects, O1 and O2, have...Ch. 22 - (II) A ring of charge with uniform charge density...Ch. 22 - (II) In a certain region of space, the electric...Ch. 22 - (II) A point charge Q is placed at the center of a...Ch. 22 - (II) A 15.0-cm-long uniformly charged plastic rod...Ch. 22 - (I) Draw the electric field lines around a...Ch. 22 - (I) The field just outside a 3.50-cm-radius metal...Ch. 22 - (I) Starting from the result of Example 223, show...Ch. 22 - (I) A long thin wire, hundreds of meters long,...Ch. 22 - (I) A metal globe has l.50 mC of charge put on it...Ch. 22 - (II) A nonconducting sphere is made of two layers....Ch. 22 - (II) A solid metal sphere of radius 3.00 m carries...Ch. 22 - (II) A 15.0-cm-diameter nonconducting sphere...Ch. 22 - (II) A flat square sheet of thin aluminum foil,...Ch. 22 - (II) A spherical cavity of radius 4.50 cm is at...Ch. 22 - (II) A point charge Q rests at the center of an...Ch. 22 - (II) A solid metal cube has a spherical cavity at...Ch. 22 - (II) Two large, flat metal plates are separated by...Ch. 22 - (II) Suppose the two conducting plates in Problem...Ch. 22 - (II) The electric field between two square metal...Ch. 22 - (II) Two thin concentric spherical shells of radii...Ch. 22 - (II) A spherical rubber balloon carries a total...Ch. 22 - (II) Suppose the nonconducting sphere of Example...Ch. 22 - (II) Suppose in Fig. 2232, Problem 29, there is...Ch. 22 - (II) Suppose the thick spherical shell of Problem...Ch. 22 - (II) Suppose that at the center of the cavity...Ch. 22 - (II) A long cylindrical shell of radius R0 and...Ch. 22 - (II) A very long solid nonconducting cylinder of...Ch. 22 - (II) A thin cylindrical shell of radius R1 is...Ch. 22 - (II) A thin cylindrical shell of radius R1 = 6.5...Ch. 22 - (II) (a) If an electron (m = 9.1 1031 kg) escaped...Ch. 22 - (II) A very long solid nonconducting cylinder of...Ch. 22 - (II) A nonconducting sphere of radius r0 is...Ch. 22 - (II) A very long solid nonconducting cylinder of...Ch. 22 - (II) A flat ring (inner radius R0, outer radius...Ch. 22 - (II) An uncharged solid conducting sphere of...Ch. 22 - (III) A very large (i.e., assume infinite) flat...Ch. 22 - (III) Suppose the density of charge between r1 and...Ch. 22 - (III) Suppose two thin flat plates measure 1.0 m ...Ch. 22 - (III) A flat slab of nonconducting material (Fig....Ch. 22 - (III) A flat slab of nonconducting material has...Ch. 22 - (III) An extremely long, solid nonconducting...Ch. 22 - (III) Charge is distributed within a solid sphere...Ch. 22 - A point charge Q is on the axis of a short...Ch. 22 - Prob. 51GPCh. 22 - The Earth is surrounded by an electric field,...Ch. 22 - A cube of side has one corner at the origin of...Ch. 22 - A solid nonconducting sphere of radius r0 has a...Ch. 22 - A point charge of 9.20 nC is located at the origin...Ch. 22 - A point charge produces an electric flux of +235 N...Ch. 22 - A point charge Q is placed a distance r0/2 above...Ch. 22 - Three large but thin charged sheets are parallel...Ch. 22 - Neutral hydrogen can be modeled as a positive...Ch. 22 - A very large thin plane has uniform surface charge...Ch. 22 - A sphere of radius r0 carries a volume charge...Ch. 22 - Dry air will break down and generate a spark if...Ch. 22 - Three very large sheets are separated by equal...Ch. 22 - In a cubical volume, 0.70 m on a side, the...Ch. 22 - A conducting spherical shell (Fig. 2249) has inner...Ch. 22 - A hemisphere of radius R is placed in a...Ch. 22 - (III) An electric field is given by...
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