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Chapter 24: Q. 43 (page 685)

Find the electric field inside and outside a hollow plastic ball of radius $R$ that has charge $Q$ uniformly distributed on its outer surface.

Short Answer

Expert verified

Electric field inside a hollow plastic ball is $0 nC$ .

Electric field outside a hollow plastic ball is $\frac{1}{4 {蟺系}_{o}} \frac{Q}{r^{2}}$ .

Step by step solution

01

Figure for Electric field inside a hollow plastic ball

Figure is,

02

Calculation for electric field inside a hollow plastic ball

Electric flux

$桅_{e} = EA = \frac{Q_{in}}{系_{o}}$

localid="1648763653778" $E = \frac{Q_{in}}{系_{o} A} . . . 1$

The charge is spread on the outside surface of a plastic sphere, which is not conductive.

As a result, the sphere's net charge is zero.

The quantity of charge in the bulk determines the electric field.

As a result of the net charge being zero.

Inside the sphere, the electric field is zero.

$E_{in} = 0 N / C$

03

Figure for Electric field outside a hollow plastic ball

Figure is,

04

Calculation for electric field outside a hollow plastic ball

The Gaussian surface enclosed net charge for a point outside the spher $+ Q$ .

The enclosed surface's area is

$A = 4 {蟺谤}^{2}$

This charge is enclosedlocalid="1648918575953" $Q_{in}$ in the gaussian surface is,

$Q_{in} = Q$

Substitute all values in equation $1$ ,

We get,

$E_{out} = \frac{Q_{in}}{系_{o} A}$

$= \frac{Q}{系_{o} (4 {蟺谤}^{2})}$

$= \frac{1}{4 {蟺系}_{o}} \frac{Q}{r^{2}}$

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Most popular questions from this chapter

The earth has a vertical electric field at the surface, pointing down, that averages $100 N / C$ . This field is maintained by various atmospheric processes, including lightning. What is the excess charge on the surface of the earth $?$

The conducting box in FIGURE EX24.26 has been given an excess negative charge. The surface density of excess electrons at the center of the top surface is $5.0 脳 10^{10} e l e c t r o n s / m^{2}$ . What are the electric field strengths $E_{1}$ to $E_{3}$ at points 1 to 3?

A $1.0 c m 脳 1.0 c m 脳 1.0 c m$ box with its edges aligned with the $x y z$ -axes is in the electric field $\overset{鈫�}{E} = (350 x + 150) \hat{i} N / C$ , where x is in meters. What is the net electric flux through the box?

What is the electric flux through the surface shown in FIGURE EX24.9?

FIGURE P $24.47$ shows an infinitely wide conductor parallel to and distance $d$ from an infinitely wide plane of charge with surface charge density $畏$ . What are the electric field ${\overset{鈫�}{E}}_{1}$ to ${\overset{鈫�}{E}}_{4}$ in regions $1$ to $4$ ?

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