   Chapter 15, Problem 46P

Chapter
Section
Textbook Problem

The electric field everywhere on the surface of a charged sphere of radius 0.230 m has a magnitude of 575 N/C and points radially outward from the center of the sphere. (a) What is the net charge on the sphere? (b) What can you conclude about the nature and distribution of charge inside the sphere?

(a)

To determine
The net charge on the sphere.

Explanation

Given info: The electric field (E) is 575 N/C. The radius of the sphere (r) is 0.230 m.

Formula to calculate the electric flux is,

ϕE=EAcosθ

From Gauss’s law,

ϕE=qinsideε0

• qinside is the charge inside the surface.
• ε0 is the permittivity of free space.

Therefore,

qinside=ε0EAcosθ

The area is,

A=4πr2

Therefore,

qinside=4πε0Er2cosθ

Substitute 8

(b)

To determine
The nature of charge distribution.

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