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Chapter 23: Q57P (page 683)

A thin-walled metal spherical shell has radius0.25cmand charge 2.88x104N/C. Find Efor a point (a) inside the shell, (b) just outside it, and (c)from the center.

Short Answer

Expert verified

a) The magnitude of the electric fieldinside the shell is zero

b) The magnitude of the electric field just outside the shell is 2.88x104N/C.

c) The magnitude of the electric field 3.00 m from the center is200N/C

Step by step solution

01

Listing the given quantities

spherical shell has a radius of 25.0 cm and charge 2.00x10-7C

02

Understanding the concept of electric field

Applying the concept of electric field for spherical shells we get the magnitude of the electric field.

Formula:

E=q4蟺蔚01r2

03

(a) Calculation of the magnitude of the electric field inside the shell

For r < R, E = 0

The magnitude of the electric field inside the shell is zero

04

(b) Calculation of the magnitude of the electric field just outside the shell

For r slightly greater than R,

E=q4蟺蔚01r2=q4蟺蔚0R2=9脳109N.m2/C22.00脳10-7C0.250m2=2.88脳104N/C

The magnitude of the electric field just outside the shell is 2.88脳104N/C.

05

(c) Calculation of the magnitude of the electric field 3.00 m from the shell

For r > R

E=q4蟺蔚01r2=ERRr2=2.88脳104N/C0.250m3.00m2=200N/C

The magnitude of the electric field 3.00 m from the center is 200N/C

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Most popular questions from this chapter

A small charged ball lies within the hollow of a metallic spherical shell of radius R . For three situations, the net charges on the ball and shell, respectively, are

(1)+4q,0;

(2)鈭�6q,+10q;

(3)+16q,鈭�12q. Rank the situations according to the charge on

(a) the inner surface of the shell and

(b) the outer surface, most positive first.

A particle of charge q=1.0脳10-7Cis at the center of a spherical cavity of radius 3.0cmin a chunk of metal. Find the electric field

(a)1.5cmfrom the cavity center and

(b) anyplace in the metal.

Charge of uniform volume densityr=1.2nC/m3fills an infinite slab between role="math" localid="1657340713406" x=-5.0cmand role="math" localid="1657340708898" x=+5.0cm.What is the magnitude of the electric field at any point with the coordinate (a) x=4.0cmand (b)x=6.0cm?

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?

Figure 23-52 gives the magnitude of the electric field inside and outside a sphere with a positive charge distributed uniformly throughout its volume. The scale of the vertical axis is set by Es=5.0脳10N/C. What is the charge on the sphere?
See all solutions

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