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Chapter 23: Q56P (page 683)

The electric field in a particular space isE鈫�=(x+2)i^N/C, with xin meters. Consider a cylindrical Gaussian surface of radius that is coaxial with the x-axis. One end of the cylinder is atx=0 . (a) What is the magnitude of the electric flux through the other end of the cylinder at X=2.0m? (b) What net charge is enclosed within the cylinder?

Short Answer

Expert verified

a) Magnitude of the electric flux through the other end of the cylinder at x = 2.0 m is 0.50N.m2/C

b) Net charge enclosed by the cylinder is 2.2x10-12C.

Step by step solution

01

Listing the given quantities

E鈫�=(x+2)i^N/C

cylindrical Gaussian surface of radius 20 cm

02

Understanding the concept of Gauss law of electrostatics

Using the statement of Gauss law determine the charge enclosed by the cylinder

03

(a) Calculations of electric flux through the other end of the cylinder at x = 2.0 m

There is no flux through the sides, so we have two contributions to the flux, one

from the x = 2.0 m end

蠒2=+2.0+2N/C蟺0.20m2=0.50N.m2/C

and one from the x = 0 end

蠒2=+(2N/C)蟺0.20m2=0.25N.m2/C

Magnitude of the electric flux through the other end of the cylinder at x = 2.0 m is0.50N.m2/C

04

(b) Calculations of charge enclosed by the cylinder

By Gauss鈥� law, we have

qenc=蔚0蠒2+蠒0=8.85脳10-12C2/N.m2脳0.25N.m2/C=2.2脳10-12C

The net charge enclosed by the cylinder is 2.2脳10-12C

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Most popular questions from this chapter

The box-like Gaussian surface shown in Fig. 23-38 encloses a net charge of+24.0蔚0Cand lies in an electric field given by role="math" localid="1657339232606" E鈫�=[(10.0+2.00)j^+bzk^]N/Cwith xand zin meters and ba constant. The bottom face is in the plane; the top face is in the horizontal plane passing through y2=1.00m. For x1=1.00m, x2=4.00m,z1=1.00m , andz2=3.00m, what is b?

Figure 23-42 is a section of a conducting rod of radiusR1=1.30mmand lengthL=11.00m inside a thin-walled coaxial conducting cylindrical shell of radiusR2=10.0R1 and the (same) length L. The net charge on the conducting rod isQ1=+3.40脳10-12; that on the shell isQ2=-2.00Q1. What are the (a) magnitude Eand (b) direction (radially inward or outward) of the electric field at radial distancer=2.00R2? What are (c) Eand (d) the direction atr=5.00R1? What is the charge on the (e) interior and (f) exterior surface of the shell?

Figure 23-57 shows a spherical shell with uniform volume charge density r=1.84nC/m3, inner radius localid="1657346086449" a=10.0cm, and outer radius b=2.00a. What is the magnitude of the electric field at radial distances (a)localid="1657346159507" r=0; (b) r=a/2.00, (c) r=a, (d) r=1.50a, (e) r=b, and (f) r=3.00b?

Figure 23-61 shows a Geiger counter, a device used to detect ionizing radiation, which causes ionization of atoms. A thin, positively charged central wire is surrounded by a concentric, circular, conducting cylindrical shell with an equal negative charge, creating a strong radial electric field. The shell contains a low-pressure inert gas. A particle of radiation entering the device through the shell wall ionizes a few of the gas atoms. The resulting free electrons (e) are drawn to the positive wire. However, the electric field is so intense that, between collisions with gas atoms, the free electrons gain energy sufficient to ionize these atoms also. More free electrons are thereby created, and the process is repeated until the electrons reach the wire. The resulting 鈥渁valanche鈥� of electrons is collected by the wire, generating a signal that is used to record the passage of the original particle of radiation. Suppose that the radius of the central wire is 25 mm, the inner radius of the shell 1.4 cm, and the length of the shell 16 cm. If the electric field at the shell鈥檚 inner wall is,2.9脳104N/C what is the total positive charge on the central wire?

A spherical ball of charged particles has a uniform charge density. In terms of the ball鈥檚 radius R, at what radial distances

(a) inside and

(b) outside the ball is the magnitude of the ball鈥檚 electric field equal to14of the maximum magnitude of that field?
See all solutions

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