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Chapter 23: Q70P (page 684)

Charge of uniform volume density 蚁=3.2鈥�渭颁/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鈥檚 center?

Short Answer

Expert verified

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

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

Step by step solution

01

Listing the given quantities

  • Volume Charge density蚁=3.2鈥�渭颁/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(43蟺谤3)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=qr4蟺蔚0R3=9.0脳109N.m2/C21.68脳10-9C0.035m0.050m3=4.2脳103N/C

The magnitude of the electric field at 3.5 cm from the center of the sphere is4.2脳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=qr4蟺蔚0R2=9.0脳109N.m2/C21.68脳10-9C0.080m2=2.4脳103N/C

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

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Most popular questions from this chapter

Space vehicles traveling through Earth鈥檚 radiation belts can intercept a significant number of electrons. The resulting charge buildup can damage electronic components and disrupt operations. Suppose a spherical metal satellite1.3min diameter accumulates2.4渭颁of charge in one orbital revolution. (a) Find the resulting surface charge density. (b) Calculate the magnitude of the electric field just outside the surface of the satellite, due to the surface charge.

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