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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

In Fig. 23-25, an electron is released between two infinite non-conducting sheets that are horizontal and have uniform surface charge densities蟽(+)and蟽(-), as indicated. The electron is subjected to the following three situations involving surface charge densities and sheet separations. Rank the magnitudes of the electron鈥檚 acceleration, greatest first.

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?

In Fig. 23-33, a proton is a distance d/2directly above the center of a square of side d. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge d.)

In Fig. 23-54, a solid sphere of radius a=2.00cmis concentric with a spherical conducting shell of inner radius b=2.00a and outer radius c=2.40a. The sphere has a net uniform charge q1=+5.00fC ; the shell has a net charge q2=-q1 . What is the magnitude of the electric field at radial distances (a) r=0, (b) r=a/2.00, (c) r=a, (d) r=1.50a, (e) r=2.30a, and (f) r=3.50a? What is the net charge on the (g) inner and (h) outer surface of the shell?

An electron is released 9.0cmfrom a very long non-conducting rod with a uniform6.0渭颁/m. What is the magnitude of the electron鈥檚 initial acceleration?
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