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Chapter 24: Q75P (page 715)

An electric field of approximately 100 V/mis often observed near the surface of Earth. If this were the field over the entire surface, what would be the electric potential of a point on the surface? (SetV=0 at infinity.)

Short Answer

Expert verified

V=6.4×108 V

Step by step solution

01

Given

Intensity of the electric fieldE=100 V/m
Radius of the earth's spherical surface,Rc=6400 km

02

Understanding the concept

Use the relation between E and V.

Electric potential at the surface of the Earth,V=14πεoqRc
Electric intensity at the surface of earth,E=14πεoqRe2=VRe

03

Calculate the electric potential  

Electric potential,

V=EReV=(100 V/m)(6400×103 m)V=6.4×108 V

Hence, the electric potential of a point on the surface is V=6.4×108 V

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Most popular questions from this chapter

Figure 24-30 shows a system of three charged particles. If you move the particle of chargefrom point Ato point D, are the following quantities positive, negative, or zero: (a) the change in the electric potential energy of the three particle system, (b) the work done by the net electric force on the particle you moved (that is, the net force due to the other two particles), and (c) the work done by your force? (d) What are the answers to (a) through (c) if, instead, the particle is moved from Bto C?

Two metal spheres, each of radius 3.0 cm, have a center-to-center separation of 2.0 m. Sphere 1 has charge +1.0×10-8C; sphere 2 has charge-3.0×10-8C. Assume that the separation is large enough for us to say that the charge on each sphere is uniformly distributed (the spheres do not affect each other). Withdata-custom-editor="chemistry" V=0at infinity, calculate (a) the potential at the point halfway between the centers and the potential on the surface of (b) sphere 1 and (c) sphere 2.

A metal sphere of radius 15cm has a net charge of3.0×10-8C . (a) What is the electric field at the sphere’s surface? (b) IfV=0 at infinity, what is the electric potential at the sphere’s surface? (c) At what distance from the sphere’s surface has the electric potential decreased by500 V ?

The magnitude E of an electric field depends on the radial distance r according toE=A/r4, where is a constant with the unit volt–cubic meter. As a multiple of A, what is the magnitude of the electric potential difference betweenr=2.00mandr=3.00m?

In Fig. 24-71, a metal sphere with chargeq=5.00μCand radius r=3.00cm is concentric with a larger metal sphere with charge Q=15.0μC and radius R=6.00cm .

(a) What is the potential difference between the spheres? If we connect the spheres with a wire, what then is the charge on

(b) the smaller sphere and

(c) the larger sphere?
See all solutions

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