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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=q14蟺蔚0rR3=q14蟺蔚0R/2R3

Outside sphere 2,

q24蟺蔚01r2=q24蟺蔚011.50R2

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

A Gaussian surface in the form of a hemisphere of radiusR=5.68cmlies in a uniform electric field of magnitudeE=2.50鈥�N/C. The surface encloses no net charge. At the (flat) base of the surface, the field is perpendicular to the surface and directed into the surface. What is the flux through

(a) the base and

(b) the curved portion of the surface?

When a shower is turned on in a closed bathroom, the splashing of the water on the bare tub can fill the room鈥檚 air with negatively charged ions and produce an electric field in the air as great as 1000N/C. Consider a bathroom with dimensions2.5m脳3.0m脳2.0m. 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 of600N/C. Also, treat those surfaces as forming a closed Gaussian surface around the room鈥檚 air. What are (a) the volume charge density r and (b) the number of excess elementary charges eper cubic meter in the room鈥檚 air?

In Fig. 23-49, a small, non-conducting ball of massm=1.0mgand charge q=2.0脳10-8C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle 胃=30owith a vertical, uniformly charged non-conducting sheet (shown in cross-section). Considering the gravitational force on the ball and assuming the sheet extends far vertically and into and out of the page, calculate the surface charge density s of the sheet.

Figure 23-34 shows a closed Gaussian surface in the shape of a cube of edge length 2.00 m. It lies in a region where the non-uniform electric field is given by E鈫�=[(3.00x+4.00)i^+6.00j^+7.00k^]N/C, with xin meters. What is the net charge contained by the cube?

What net charge is enclosed by the Gaussian cube of Problem 2?
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