Two particles 1 and 2, each carrying 6.0 nC of charge, are located along an x axis, one particle atx=−30 mm and the other at x = 30 mm. Where along the y axis is a particle 3 carrying a charge of +2.0 nC if it experiences an electric force of 6.9 × 10^−5 N ȷ^?
Coulomb's law: F = (k*q1*q2)/d^2
Pythagorean Theorm: c = SQRT((a^2) + b^2))
The Attempt at a Solution
So I know the answer is 10mm and 40mm. However, throughout my work, I am not even close to said values. Here is the work I have done:
Some notes on my progress:
1.) I first began by finding Fx (since Fy was defined in the problem as 6.9x10^-5, and was split since I only need the force of a single 6.0 nC charge).
2.) After calculating this value, I took both force vectors and added them together to obtain the final total Force between particle 1 or 2 and particle 3.
3.) Taking this force value, I plugged it back into Coulomb's law in an attempt to obtain the value of d (In this problem, x = 30mm, y is what I am trying to find. So by finding d, I can use Pythagorean to calculate it). However... this is where things break apart. When I find d, I realize that this value is SMALLER than my x value... which makes 0 sense. From here I became absolutely lost.
If someone could guide me from this point, I would greatly appreciate it! Thank you!