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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 is6碍蔚0r3

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=qenc4蟺蔚0r2=14蟺蔚0r2鈭�01蚁r4蟺谤2dr

To solve for 蚁rand obtain,

role="math" localid="1657353658777" 蚁r=蔚0r2ddrr2Er=蔚0r2ddrKr6=6碍蔚0r3

The volume charge density is6碍蔚0r3

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Most popular questions from this chapter

The electric field in a particular space isE鈫�=(x+2)i^N/C, with xin meters. Consider a cylindrical Gaussian surface of radius that is coaxial with the x-axis. One end of the cylinder is atx=0 . (a) What is the magnitude of the electric flux through the other end of the cylinder at X=2.0m? (b) What net charge is enclosed within the cylinder?

An isolated conductor has net charge+10脳10-6Cand a cavity with a particle of charge=+3.0脳10-6CWhat is the charge on (a) the cavity wall and (b) the outer surface?

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?

Assume that a ball of charged particles has a uniformly distributed negative charge density except for a narrow radial tunnel through its center, from the surface on one side to the surface on the opposite side. Also assume that we can position a proton anywhere along the tunnel or outside the ball. Let Fr be the magnitude of the electrostatic force on the proton when it is located at the ball鈥檚 surface, at radius R. As a multiple of R, how far from the surface is there a point where the force magnitude is if we move the proton (a) away from the ball and (b) into the tunnel?

A non-conducting solid sphere has a uniform volume charge density P. Letr鈫�be the vector from the center of the sphere to a general point Pwithin the sphere.

(a) Show that the electric field at Pis given byE鈨�=蚁r鈨�/3蔚0(Note that the result is independent of the radius of the sphere.)

(b) A spherical cavity is hollowed out of the sphere, as shown in Fig. 23- 60. Using superposition concepts, show that the electric field at all points within the cavity is uniform and equal to E鈨�=蚁r鈨�/3蔚0where ais the position vector from the center of the sphere to the center of the cavity.
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