Three point charges are arranged along the x-axis. charge q1 = +3.00 μc is at the origin, and charge q2 = -5.00 μc is at x = 0.200 m. charge q3 = -8.00 μc. where is q3 located if the net force on q1 is 7.00 n in the -x-direction?

q₃ is located at X= - 0.144m

Explanation:

Coulomb law:

Two point charges (q1, q2) separated by a distance (d) exert a mutual force (F) whose magnitude is determined by the following formula:

F=K*q₁*q₂/d² Formula (1)  

F: Electric force in Newtons (N)

K : Coulomb constant in N*m²/C²

q₁, q₂: Charges in Coulombs (C)  

d: distance between the charges in meters(m)

Equivalence  

1uC= 10⁻⁶C

Data

F=0.66 N

K=8.99x10⁹N*m²/C²

q₁ =  +3.00 μC = +3.00  *10⁻⁶C

q₂=  -5.00  μC =  -5.00  *10⁻⁶C

q₃= -8.00 μC= -8.00 *10⁻⁶C

d₁₂= 0.2m: distance between q₁ and q₂

Fn=7 N: Net force on q₁

Calculation of the magnitude of the forces exerted on q₁

F₂₁ = K*q₁*q₂/d₁₂² = (8.99 * 10⁹ * 3.00 * 10⁻⁶ * 5.00 * 10⁻⁶)/(0.2)² = 3.37 N

F₃₁ = K*q₁*q₃/d₁₃² = (8.99 * 10⁹ * 3.00 * 10⁻⁶ * 8.00 * 10⁻⁶)/(d₁₃)² = 0.21576/(d₁₃)² N

Calculation of the distance d₁₃ between q₁ and q₃

In order for the net force to be negative on the x axis, the charge q₃ must be located on the x axis to the left of the charge q₁

F₂₁: It is a force of attraction and goes to the right(+)

F₃₁: It is a force of attraction and goes to the left(-)

-Fn₁ = F₂₁ - F₃₁

-7 = 3.37 - 0.21576/(d₁₃)²

3.37 + 7 = 0.21576/(d₁₃)²

10.37*(d₁₃)²=0.21576

(d₁₃)² = (0.215769 )/ (10.37)

(d₁₃)² =  20.8 * 10⁻³

d₁₃=0.144m

q₃ is located at X= - 0.144m

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