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Chapter 23: Q70P (page 684)

Charge of uniform volume density ρ=3.2 μC/m3 fills a nonconducting solid sphere of radius5.0cm. . What is the magnitude of the electric field

(a) 3.5cmand

(b) 8.0cmfrom the sphere’s center?

Short Answer

Expert verified

a) The magnitude of the electric fieldat3.5 cm from the center of the sphereis4.2×103 N/C .

b) The magnitude of the electric field at 8.0 cm from the center of the sphere is2.4×103 N/C .

Step by step solution

01

Listing the given quantities

  • Volume Charge densityρ=3.2 μC/m3
  • radius of the sphere = 5.0 cm
02

Understanding the concept of charge density and electric field

Since the charge distribution is uniform, we can find the total charge q by multiplying by the spherical volume(43πr3)with r = R = 0.050 m.

This gives q = 1.68 nC.

03

Step 3: (a) Calculations for the magnitude of the electric field at r = 3.5 cm from the center of the sphere

Given r = 0.035 m.

The electric field can be calculated as:

Einternal=qr4πε0R3=9.0×109N.m2/C21.68×10-9C0.035m0.050m3=4.2×103N/C

The magnitude of the electric field at 3.5 cm from the center of the sphere is4.2×103N/C .

04

(b) Calculations for the magnitude of the electric field at r=8.0 cm from the center of the sphere

Outside the sphere, we have (with r = 0.080 m), then the electric field can be calculated as:

Einternal=qr4πε0R2=9.0×109N.m2/C21.68×10-9C0.080m2=2.4×103N/C

The magnitude of the electric field at 8.0 cm from the center of the sphere is 2.4×103N/C.

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Most popular questions from this chapter

A non-conducting solid sphere has a uniform volume charge density P. Letr→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 byE⃗=ρr⃗/3ε0(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 E⃗=ρr⃗/3ε0where ais the position vector from the center of the sphere to the center of the cavity.

A charged particle is held at the center of a spherical shell. Figure 23-53 gives the magnitude Eof the electric field versus radial distance r. The scale of the vertical axis is set by Es=10×107N/C. Approximately, what is the net charge on the shell?

Charge is distributed uniformly throughout the volume of an infinitely long solid cylinder of radius R.

(a) Show that, at a distance r < R from the cylinder axis,E=pr2ε0where is the volume charge density.

(b) Write an expression for E when r > R.

In Fig. 23-56, a non conducting spherical shell of inner radius a=2.00cm and outer radius b=2.40cm has (within its thickness) a positive volume charge density r=A/r , where Ais a constant and ris the distance from the center of the shell. In addition, a small ball of charge q=45.0fC is located at that center. What is value should Ahave if the electric field in the shell ( a≤r≤b) is to be uniform?

Figure 23-26 shows four situations in which four very long rods extend into and out of the page (we see only their cross sections). The value below each cross-section gives that particular rod’s uniform charge density in micro-coulombs per meter. The rods are separated by either d or role="math" localid="1661874332860" 2das drawn, and a central point is shown midway between the inner rods. Rank the situations according to the magnitude of the net electric field at that central point, greatest first.
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