Fundamentals Of Physics
11th Edition
ISBN: 9781119573968
Author: David Halliday
Publisher: WILEY
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Chapter 23, Problem 8P
When a shower is turned on in a dosed bathroom, the splashing of the water on the bare tub can fill the room’s air with negatively charged ions and produce an electric field in the air as great as 1000 N/C. Consider a bathroom with dimensions 2.5 m × 3.0 m × 2.0 m. Along the ceiling, floor, and four walls, approximate the electric field in the air as being directed perpendicular to the surface and as having a uniform magnitude of 600 N/C. Also, treat those surfaces as forming a closed Gaussian surface around the room’s air. What are (a) the volume charge density ρ and (b) the number of excess elementary charges e per cubic meter in the room’s air?
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Part A
m
2πkT
) 3/2
Calculate the integral (v) = f vƒ (v)dv. The function f(v) describing the actual distribution of molecular speeds is called the Maxwell-Boltzmann distribution,
=
ƒ(v) = 4π (· v²e-mv²/2kT
. (Hint: Make the change of variable v² =x and use the tabulated integral foxne
integer and a is a positive constant.)
Express your answer in terms of the variables T, m, and appropriate constants.
-ax dx
n!
-
an+1
where n is a positive
(v)
=
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Chapter 23 Solutions
Fundamentals Of Physics
Ch. 23 - A surface has the area vector A = 2 i 3 j m2....Ch. 23 - Figure 23-22 shows, in cross section, three solid...Ch. 23 - Figure 23-23 shows, in cross section, a central...Ch. 23 - Figure 23-24 shows, in cross section, two Gaussian...Ch. 23 - In Fig. 23-25, an election is released between two...Ch. 23 - Three infinite nonconducting sheets, with uniform...Ch. 23 - Figure 23-26 shows four situations in which four...Ch. 23 - Figure 23-27 shows four solid spheres, each with...Ch. 23 - A small charged ball lies within the hollow of a...Ch. 23 - Rank the situations of Question 9 according to the...
Ch. 23 - Figure 23-28 shows a section of three long charged...Ch. 23 - Figure 23-29 shows four Gaussian surfaces...Ch. 23 - SSM The square surface shown in Fig. 23-30...Ch. 23 - An electric field given by E = 4.0 i 3.0y2 2.0 j...Ch. 23 - The cube in Fig. 23-31 has edge length 1.40 m and...Ch. 23 - In Fig. 23-32, a butterfly net is in a uniform...Ch. 23 - In Fig. 23-33, a proton is a distance d/2 directly...Ch. 23 - At each point on the surface of the cube shown in...Ch. 23 - A particle of charge 1.8 C is at the center of a...Ch. 23 - When a shower is turned on in a dosed bathroom,...Ch. 23 - Prob. 9PCh. 23 - Figure 23-34 shows a closed Gaussian surface in...Ch. 23 - GO Figure 23-35 shows a dosed Gaussian surface in...Ch. 23 - Figure 23-36 shows two non-conducting spherical...Ch. 23 - SSM The electric field in a certain region of...Ch. 23 - GO Flux and nonconducting shells. A charged...Ch. 23 - A particle of charge q is placed at one corner of...Ch. 23 - GO The box-like Gaussian surface shown in Fig....Ch. 23 - SSM A uniformly charged conducting sphere of 1.2 m...Ch. 23 - The electric field just above the surface of the...Ch. 23 - Space vehicles traveling through Earths radiation...Ch. 23 - GO Flux and conducting shells. A charged particle...Ch. 23 - An isolated conductor has net charge 10 106 C and...Ch. 23 - An electron is released 9.0 cm from a very long...Ch. 23 - a The drum of a photocopying machine has a length...Ch. 23 - Figure 23-40 shows a section of a long,...Ch. 23 - SSM An infinite line of charge produces a field of...Ch. 23 - Figure 23-41a shows a narrow charged solid...Ch. 23 - GO A long, straight wire has fixed negative charge...Ch. 23 - GO A charge of uniform linear density 2.0 nC/m is...Ch. 23 - SSM WWW Figure 23-42 is a section of a conducting...Ch. 23 - In Fig. 23-43, short sections of two very long...Ch. 23 - ILW Two long, charged, thin-walled, concentric...Ch. 23 - GO A long, nonconducting, solid cylinder of radius...Ch. 23 - In Fig. 23-44, two large, thin metal plates are...Ch. 23 - In Fig. 23-45, a small circular hole of radius R =...Ch. 23 - GO Figure 23-46a shows three plastic sheets that...Ch. 23 - Figure 23-47 shows cross sections through two...Ch. 23 - SSM WWW A square metal plate of edge length 8.0 cm...Ch. 23 - GO In Fig. 23-48a, an electron is shot directly...Ch. 23 - SSM In Fig. 23-49, a small, nonconducting ball of...Ch. 23 - Figure 23-50 shows a very large nonconducting...Ch. 23 - GO An electron is shot directly toward the center...Ch. 23 - Two large metal plates of area 1.0 m2 face each...Ch. 23 - GO Figure 23-51 shows a cross section through a...Ch. 23 - Figure 23-52 gives the magnitude of the electric...Ch. 23 - Two charged concentric spherical shells have radii...Ch. 23 - Assume that a ball of charged particles has a...Ch. 23 - SSM An unknown charge sits on a conducting solid...Ch. 23 - Prob. 48PCh. 23 - In Fig, 23-54, a solid sphere of radius a = 2.00...Ch. 23 - GO Figure 23-55 shows two nonconducting spherical...Ch. 23 - SSM WWW In Fig. 23-56, a nonconducting spherical...Ch. 23 - GO Figure 23-57 shows a spherical shell with...Ch. 23 - ILW The volume charge density of a solid...Ch. 23 - Figure 23-58 shows, in cross section, two solid...Ch. 23 - A charge distribution that is spherically...Ch. 23 - The electric field in a particular space is E = x ...Ch. 23 - A thin-walled metal spherical shell has radius...Ch. 23 - A uniform surface charge of density 8.0 nC/m2 is...Ch. 23 - Charge of uniform volume density = 1.2 nC/m3...Ch. 23 - The chocolate crumb mystery. Explosions ignited by...Ch. 23 - SSM A thin-walled metal spherical shell of radius...Ch. 23 - A particle of charge q = 1.0 107 C is at the...Ch. 23 - A proton at speed v = 3.00 105 m/s orbits at...Ch. 23 - Equation 23-11 E = /0 gives the electric field at...Ch. 23 - Charge Q is uniformly distributed in a sphere of...Ch. 23 - A charged particle causes an electric flux of 750...Ch. 23 - SSM The electric field at point P just outside the...Ch. 23 - The net electric flux through each face of a die...Ch. 23 - Figure 23-59 shows, in cross section, three...Ch. 23 - Charge of uniform volume density = 3.2 C/m3 fills...Ch. 23 - A Gaussian surface in the form of a hemisphere of...Ch. 23 - What net charge is enclosed by the Gaussian cube...Ch. 23 - A nonconducting solid sphere has a uniform volume...Ch. 23 - A uniform charge density of 500 nC/m3 is...Ch. 23 - Figure 23-61 shows a Geiger counter, a device used...Ch. 23 - Charge is distributed uniformly throughout the...Ch. 23 - SSM A spherical conducting shell has a charge of...Ch. 23 - A charge of 6.00 pC is spread uniformly throughout...Ch. 23 - Water in an irrigation ditch of width w = 3.22 m...Ch. 23 - Charge of uniform surface density 8.00 nC/m2 is...Ch. 23 - A spherical ball at charged particles has a...
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