Consider the three point charges in the x-yplane as shown in the figure.y (cm)9080706050403020100Q1Q20 10 20 3040 50 60 70 80 90x (cm)What is the total electrostatic energy of thesystem? The point charges have the followingvalues: Q₁ = 5.01 nC, Q₂ = 6.47 nC, Q3 =-7.60 nC.Point charge Q3 is moved away to infinity byan external force. How much work did theexternal force perform in this process?

Answered: What is the total electrostatic energy…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Consider the three point charges in the x-y
plane as shown in the figure.
y (cm)
90
80
70
60
50
40
30
20
10
0
Q1
Q2
0 10 20 30
40 50 60 70 80 90
x (cm)
What is the total electrostatic energy of the
system? The point charges have the following
values: Q₁ = 5.01 nC, Q₂ = 6.47 nC, Q3 =
-7.60 nC.
Point charge Q3 is moved away to infinity by
an external force. How much work did the
external force perform in this process?

Expert Solution

Step 1: electrostatic energy of a system of charges

The electrostatic energy of a system of charges, you can use the formula for the electrostatic potential energy:

$U equals fraction numerator 1 over denominator 4 straight pi straight epsilon subscript 0 end fraction sum from i equals 1 to N of sum from j equals 1 to N of open parentheses fraction numerator q subscript i q subscript j over denominator r subscript i j end subscript end fraction close parentheses$

where:

U is the electrostatic potential energy of the system.
$epsilon subscript 0$ is the vacuum permittivity constant (8.854187817× $10 to the power of negative 12 end exponent$ $C squared divided by N. m squared$ )
N is the number of charges in the system.
$q subscript i comma end subscript q subscript j$ are the magnitudes of the charges.
$r subscript i j end subscript$ is the distance between two charges
in the given situation:

$r subscript 1 equals open parentheses 10 c m comma space 20 c m close parentheses semicolon space r subscript 2 equals open parentheses 80 c m space comma 30 c m close parentheses semicolon space r subscript 3 equals open parentheses 40 c m comma space 80 c m close parentheses$

the distance between charges Q₁ and Q_2:

$table row cell r subscript 12 equals square root of left parenthesis 80 text cm end text minus 10 text cm end text right parenthesis squared plus left parenthesis 30 text cm end text minus 20 text cm end text right parenthesis squared end root end cell row cell r subscript 12 equals square root of left parenthesis 70 text cm end text right parenthesis squared plus left parenthesis 10 text cm end text right parenthesis squared end root end cell row cell r subscript 12 equals 70.71 text cm end text end cell end table$

Calculate the distance between charges Q₂ and Q_3..

$table row cell r subscript 23 equals square root of left parenthesis 40 text cm end text minus 80 text cm end text right parenthesis squared plus left parenthesis 80 text cm end text minus 30 text cm end text right parenthesis squared end root end cell row cell r subscript 23 equals square root of left parenthesis negative 40 text cm end text right parenthesis squared plus left parenthesis 50 text cm end text right parenthesis squared end root end cell row cell r subscript 23 equals 64.031 text cm end text end cell end table$

Calculate the distance between charges Q₃ and Q₁.

$table row cell r subscript 31 equals square root of left parenthesis negative 40 text cm+ end text 10 text cm end text right parenthesis squared plus left parenthesis negative 80 text cm+ end text 20 text cm end text right parenthesis squared end root end cell row cell r subscript 31 equals square root of left parenthesis negative 30 text cm end text right parenthesis squared plus left parenthesis negative 60 text cm end text right parenthesis squared end root end cell row cell r subscript 31 equals 67.08 text cm end text end cell end table$

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