   # (a) A stationary charged particle at the origin creates an electric flux of 487 N · m 2 /C through any closed surface surrounding the charge. Find the electric field it creates in the empty space around it as a function of radial distance r away from the particle. (b) A small source at the origin emits an electromagnetic wave with a single frequency into vacuum, equally in all directions, with power 25.0 W. Find the electric field amplitude as a function of radial distance away from the source. (c) At what distance is the amplitude of the electric field in the wave equal to 3.00 MV/m, representing the dielectric strength of air? (d) As the distance from the source doubles, what happens to the field amplitude? (c) State how the behavior shown in part (d) compares with the behavior of the field in part (a). ### Physics for Scientists and Enginee...

9th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305116399

#### Solutions

Chapter
Section ### Physics for Scientists and Enginee...

9th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305116399
Chapter 34, Problem 34.68AP
Textbook Problem
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## (a) A stationary charged particle at the origin creates an electric flux of 487 N · m2/C through any closed surface surrounding the charge. Find the electric field it creates in the empty space around it as a function of radial distance r away from the particle. (b) A small source at the origin emits an electromagnetic wave with a single frequency into vacuum, equally in all directions, with power 25.0 W. Find the electric field amplitude as a function of radial distance away from the source. (c) At what distance is the amplitude of the electric field in the wave equal to 3.00 MV/m, representing the dielectric strength of air? (d) As the distance from the source doubles, what happens to the field amplitude? (c) State how the behavior shown in part (d) compares with the behavior of the field in part (a).

(a)

To determine
The electric field in the empty space as a function of radial distance r .

### Explanation of Solution

Given info: The electric flux of the particle is 487Nm2/C .

The formula to calculate the electric flux is,

ϕ=EA

Here,

E is the electric field amplitude.

A is the surface area at the origin.

Rewrite the above equation to find the value of E .

E=ϕA

Substitute 487Nm2/C for F and 4πr2 for A in the above equation to find the value of E

(b)

To determine
The electric field in the empty space as a function of radial distance r when the power is 25.0W .

(c)

To determine
The distance at which the amplitude of electric field is 3.00MV/m .

(d)

To determine
The change in the field amplitude when the distance from the source doubles.

(e)

To determine
The comparison of the behavior of filed when in vacuum as compared to that of closed surface.

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