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Three-point charges are arranged along the x-axis. Chargeq1=+3.00μCis at the origin, and chargeq2=-5.00μC is at x = 0.200 m. Chargeq3=-8.00μC. Where isq3 located if the net force onq1is 7.00 N in the -x-direction?

Short Answer

Expert verified

Chargeq3is located at-0.144m..

Step by step solution

01

Step 1:

Given data:

q1=3.0μC=3.0×106Catx1=0mq2=5μC=5.0×106Catx2=0.2mq3=8μC=8.0×106C

Net force is

F1=-7N

andK=8.989×109Nm/C2

02

Step 2:

As the third charge is positioned to the left of the first charge, thus the charge is directed towards x-direction. And electrical force between the first and second charge is an attractive force and also between the first and third charge.

So, to find net force on first charge by using Newton's Second Law.

F1=Kq1q2r12Kq1q3r22

As r1is the distance between two charges,

role="math" localid="1668158352531" r1=x2x1,r2=x3x1ifx1=0r1=x2andr2=x3F1=Kq1q2x22Kq1q3x32

03

Step 3:

Solving for x3

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 on the first charge is to the left, negative x-direction,

Thus, using the negative root,

x3=-0.144m

Hence, Charge q3is located at x3=-0.144m.

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