(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Three charges with magnitude [tex]8 × 10^{-4} C[/tex] are located at (1, 0), (0 , 0), and (-1, 0) meters. The middle charge is negative, and the other two positive. What is the net Coulombic force exerted by them on a negative [tex]8 × 10^{-5} C[/tex] charge at (0, 2)?

[tex]k = 9.0 × 10^9 N∙m^2/C^2[/tex]

2. Relevant equations

[tex]F_{12} = \frac{k |q_1| |q_2|}{r^2}[/tex]

[tex]F_{net on x} = F_{1 on x} + F_{2 on x} + F_{3 on x} + ...[/tex]

[tex]F_{net} = \sqrt {F_x^2 + F_y^2}[/tex]

3. The attempt at a solution

[tex]F_1 = \frac {(9 × 10^9)(8 × 10^{-4})(-8 × 10^{-5})}{(\sqrt{5})^2} = -115.2 (N)[/tex]

[tex]F_2 = \frac {(9 × 10^9)(-8 × 10^{-4})(-8 × 10^{-5})}{(2)^2} = 144 (N)[/tex]

[tex]F_3 = \frac {(9 × 10^9)(8 × 10^{-4})(-8 × 10^{-5})}{(\sqrt{5})^2} = -115.2 (N)[/tex]

[tex]F_x = 115.2 * sin \theta + (-115.2 * sin \theta) = 115.2 * \frac{1}{\sqrt 5} - 115.2 * \frac{1}{\sqrt 5} = 0[/tex]

[tex]F_y = -115.2 * cos \theta + (-115.2 * cos \theta) + 144 = -115.2 * \frac{1}{\sqrt 5} - -115.2 * \frac{1}{\sqrt 5} + 144 = -62.08 (N)[/tex]

[tex]F_{net} = \sqrt {F_x^2 + F_y^2} = \sqrt {0^2 + (-62.08)^2} = 62.08 (N) [/tex]

I'm pretty sure I need the magnitudes of the forces, but not sure what to do after that. I'm also not sure what should be positive or negative. The answer choices are in the 600s and 800s, and no matter what combination of positives or negatives I use, I can't get anywhere close to 600 or 800.

I attached the diagram I drew below.

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# Homework Help: Finding Net Coulombic Force

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