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Chapter 23: Q54P (page 683)

Figure 23-58 shows, in cross-section, two solid spheres with uniformly distributed charges throughout their volumes. Each has radius R. Point Plies on a line connecting the centers of the spheres, at radial distance from the center of sphere 1. If the net electric field at point Pis zero, what is the ratio of the total charges?

Short Answer

Expert verified

The ratio of total charges q2/q1 is 1.125

Step by step solution

01

Listing the given quantities

At radial distance R/2 from the center of sphere 1, the net electric field is zero.

02

Understanding the concept of electric field

Using the concept of charge distribution

03

Calculations for the ratio of charges

Inside sphere 1 we have

E=q14πε0rR3=q14πε0R/2R3

Outside sphere 2,

q24πε01r2=q24πε011.50R2

Equating both we get,

q2q1=98=1.125

The ratio of total charges q2/q1 is 1.125

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Most popular questions from this chapter

Figure 23-29 shows four Gaussian surfaces consisting of identical cylindrical midsections but different end caps. The surfaces are in a uniform electric fieldE→that is directed parallel to the central axis of each cylindrical midsection. The end caps have these shapes:S1, convex hemispheres;S3, concave hemispheres;S3, cones;S4, flat disks. Rank the surfaces according to (a) the net electric flux through them and (b) the electric flux through the top end caps, greatest first.

Figure 23-23 shows, in cross section, a central metal ball, two spherical metal shells, and three spherical Gaussian surfaces of radii R, 2R, and 3R, all with the same center. The uniform charges on the three objects are: ball, Q; smaller shell, 3Q; larger shell, 5Q. Rank the Gaussian surfaces according to the magnitude of the electric field at any point on the surface, greatest first.

Chargeis uniformly distributed in a sphere of radius R.

(a) What fraction of the charge is contained within the radius is r = R/2.00?

(b) What is the ratio of the electric field magnitude at r=R/2.00to that on the surface of the sphere?

Charge of uniform surface density 8.00nC/m2is distributed over an entire x-yplane; charge of uniform surface densityis 3.00nC/m2distributed over the parallel plane defined by z = 2.00 m. Determine the magnitude of the electric field at any point having a z-coordinate of

(a)1.00 m and

(b) 3.00 m.

The box-like Gaussian surface shown in Fig. 23-38 encloses a net charge of+24.0ε0Cand lies in an electric field given by role="math" localid="1657339232606" E→=[(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?
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