Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 24, Problem 24.6OQ
A large, metallic, spherical shell has no net charge. It is supported on an insulating stand and has a small hole at the top. A small tack with charge Q is lowered on a silk thread through the hole into the interior of the shell, (i) What is the charge on the inner surface of the shell, (a) Q (b) Q/2 (c) 0 (d) -Q/2 or (e) -Q? Choose your answers to the following questions from the same possibilities, (ii) What is The charge on the outer surface of the shell? (iii) The tack is now allowed to touch the interior surface of the shell. After this contact, what is the charge on the tack? (iv) What is the charge on the inner surface of the shell now? (v) What is the charge on the outer surface of the shell now?
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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.
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Chapter 24 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
Ch. 24 - Suppose a point charge is located at the center of...Ch. 24 - If the net flux through a gaussian surface is...Ch. 24 - A cubical gaussian surface surrounds a long,...Ch. 24 - A coaxial cable consists of a long, straight...Ch. 24 - In which of the following contexts ran Gausss law...Ch. 24 - A particle with charge q is located inside a...Ch. 24 - Charges of 3.00 nC, -2.00 nC, -7.00 nC, and 1.00...Ch. 24 - A large, metallic, spherical shell has no net...Ch. 24 - Two solid spheres, both of radius 5 cm. carry...Ch. 24 - A uniform electric field of 1.00 N/C is set up by...
Ch. 24 - A solid insulating sphere of radius 5 cm carries...Ch. 24 - A cubical gaussian surface is bisected by a large...Ch. 24 - Rank the electric fluxes through each gaussian...Ch. 24 - Consider an electric field that is uniform in...Ch. 24 - A cubical surface surrounds a point charge q...Ch. 24 - A uniform electric field exists in a region of...Ch. 24 - If the total charge inside a closed surface is...Ch. 24 - Explain why the electric flux through a closed...Ch. 24 - If more electric field lines leave a gaussian...Ch. 24 - A person is placed in a large, hollow, metallic...Ch. 24 - Consider two identical conducting spheres whose...Ch. 24 - A common demonstration involves charging a rubber...Ch. 24 - On the basis of the repulsive nature of the force...Ch. 24 - The Sun is lower in the sky during the winter than...Ch. 24 - A flat surface of area 3.20 m2 is rotated in a...Ch. 24 - A vertical electric field of magnitude 2.00 104...Ch. 24 - A 40.0-cm-diameter circular loop is rotated in a...Ch. 24 - Consider a closed triangular box resting within a...Ch. 24 - An electric field of magnitude 3.50 kN/C is...Ch. 24 - A nonuniform electric field is given by the...Ch. 24 - An uncharged, nonconducting, hollow sphere of...Ch. 24 - Find the net electric flux through the spherical...Ch. 24 - The following charges are located inside a...Ch. 24 - The electric field everywhere on the surface of a...Ch. 24 - Four closed surfaces, S1 through S4 together with...Ch. 24 - A charge of 170 C is at the center of a cube of...Ch. 24 - In the air over a particular region at an altitude...Ch. 24 - A particle with charge of 12.0 C is placed at the...Ch. 24 - (a) Find the net electric flux through the cube...Ch. 24 - (a) A panicle with charge q is located a distance...Ch. 24 - An infinitely long line charge having a uniform...Ch. 24 - Find the net electric flux through (a) the closed...Ch. 24 - A particle with charge Q = 5.00 C is located at...Ch. 24 - A particle with charge Q is located at the center...Ch. 24 - A particle with charge Q is located a small...Ch. 24 - Figure P23.23 represents the top view of a cubic...Ch. 24 - In nuclear fission, a nucleus of uranium-238,...Ch. 24 - The charge per unit length on a long, straight...Ch. 24 - A 10.0-g piece of Styrofoam carries a net charge...Ch. 24 - Determine the magnitude of the electric field at...Ch. 24 - A large, flat, horizontal sheet of charge has a...Ch. 24 - Suppose you fill two rubber balloons with air,...Ch. 24 - Consider a thin, spherical shell of radius 14.0 cm...Ch. 24 - A nonconducting wall carries charge with a uniform...Ch. 24 - A uniformly charged, straight filament 7.00 m in...Ch. 24 - Assume the magnitude of the electric field on each...Ch. 24 - Consider a long, cylindrical charge distribution...Ch. 24 - A cylindrical shell of radius 7.00 cm and length...Ch. 24 - A solid sphere of radius 40.0 cm has a total...Ch. 24 - Review. A particle with a charge of 60.0 nC is...Ch. 24 - A long, straight metal rod has a radius of 5.00 cm...Ch. 24 - Why is the following situation impossible? A solid...Ch. 24 - A solid metallic sphere of radius a carries total...Ch. 24 - A positively charged panicle is at a distance R/2...Ch. 24 - A very large, thin, flat plate of aluminum of area...Ch. 24 - In a certain region of space, the electric field...Ch. 24 - Two identical conducting spheres each having a...Ch. 24 - A square plate of copper with 50.0-cm sides has no...Ch. 24 - A long, straight wire is surrounded by a hollow...Ch. 24 - A thin, square, conducting plate 50.0 cm on a side...Ch. 24 - A solid conducting sphere of radius 2.00 cm has a...Ch. 24 - Consider a plane surface in a uniform electric...Ch. 24 - Find the electric flux through the plane surface...Ch. 24 - A hollow, metallic, spherical shell has exterior...Ch. 24 - A sphere of radius R = 1.00 m surrounds a particle...Ch. 24 - A sphere of radius R surrounds a particle with...Ch. 24 - A very large conducting plate lying in the xy...Ch. 24 - A solid, insulating sphere of radius a has a...Ch. 24 - A solid insulating sphere of radius a = 5.00 cm...Ch. 24 - Two infinite, nonconducting sheets of charge are...Ch. 24 - For the configuration shown in Figure P24.45,...Ch. 24 - An insulating solid sphere of radius a has a...Ch. 24 - A uniformly charged spherical shell with positive...Ch. 24 - An insulating solid sphere of radius a has a...Ch. 24 - A slab of insulating material has a nonuniform...Ch. 24 - Prob. 24.62CPCh. 24 - A dosed surface with dimensions a = b= 0.400 111...Ch. 24 - A sphere of radius 2a is made of a nonconducting...Ch. 24 - A spherically symmetric charge distribution has a...Ch. 24 - A solid insulating sphere of radius R has a...Ch. 24 - An infinitely long insulating cylinder of radius R...Ch. 24 - A particle with charge Q is located on the axis of...Ch. 24 - Review. A slab of insulating material (infinite in...
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