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Chapter 23: Q55P (page 683)

A charge distribution that is spherically symmetric but not uniform radially produces an electric field of magnitudeE=Kr4, directed radially outward from the center of the sphere. Here ris the radial distance from that center, andKis a constant. What is the volume density r of the charge distribution?

Short Answer

Expert verified

The volume charge density is6Kε0r3

Step by step solution

01

Listing the given quantities

E=Kr4

02

Understanding the concept of charge density and electric field

Using the formula of volume charge density and electric field determine the volume charge density

03

Explanation

We use,

E=qenc4πε0r2=14πε0r2∫01ρr4πr2dr

To solve for ρrand obtain,

role="math" localid="1657353658777" ρr=ε0r2ddrr2Er=ε0r2ddrKr6=6Kε0r3

The volume charge density is6Kε0r3

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Most popular questions from this chapter

Figure 23-47 shows cross-sections through two large, parallel, non-conducting sheets with identical distributions of positive charge with surface charge densityσ=1.77×10-22C/m2. In unit-vector notation, what is the electric field at points (a) above the sheets, (b) between them, and (c) below them?

Figure 23-51 shows a cross-section through a very large non-conducting slab of thicknessd=9.40mmand uniform volume charge density p=5.80fC/m3 . The origin of an x-axis is at the slab’s center. What is the magnitude of the slab’s electric field at an xcoordinate of (a) 0 , (b) 2.0mm , (c) 4.70mm , and (d) 26.0mm?

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?

An electric field given by E=4.0i^-3.0(y2+2.0)j^, pierces a Gaussian cube of edge length 2.0mand positioned as shown in Fig. 23-7. (The magnitude Eis in Newton per coulomb and the position xis in meters.) What is the electric flux through the (a) top face, (b) bottom face, (c) left face, and (d) back face? (e) What is the net electric flux through the cube?

In Fig. 23-49, a small, non-conducting ball of massm=1.0mgand charge q=2.0×10-8C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle θ=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.
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