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Repeat Exercise 21.17 for q3=8.00μC.

Short Answer

Expert verified

Charge q3is located at +0.144m

Step by step solution

01

Step 1:

q1=3.0μC=3.0×106Catx1=0mq2=5μC=5.0×106Catx2=0.2mq3=+8μC=8.0×106CF1=7NandK=8.989×109Nm2/C2

02

Step 2:

Here the third charge is positioned at the right of the first charge, as the net force exerted by the first is towards negative x-direction. As the electrical force between the first and second charge is attractive, therefore the force between the first and third charge is repulsive.

By using the Newton’s Second Law;

F1=F2on1F3on1

Applying coulomb law;

F1=Kq1q2r12Kq1q3r22

As r1is the distance between two charges,

r1=x2x1,r2=x3x1ifx1=0r1=x2andr2=x3F1=Kq1q2x22Kq1q3x32

03

Step 3:

Solving for x3

localid="1668414341308" F1Kq1q2x22=Kq1q3x32x32F1Kq1q2x22=Kq1q3x3=±Kq1q3F1Kq1q2x22

By putting all the values,

x3=±+8.988×109×3×106×8×1067.08.988×109×3×106×5×106(0.2)2x3=±0.144m

As the net force exerted by the first charge is towards the left negative x-direction, the force exerted by the third charge is a repulsive force, and it is towards the right of the first charge.

So due to the positive root x3=+0.144m

Hence, Charge q3is located at localid="1668414346613" +0.144m.

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