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A typical problem assigned to students is where there are two charges on the x axis and find the location of a third charge so that the net force on it is zero or some other force value given. I am wondering what is the idea behind this problem? It can get really complicated when trying to solve this. Or is there another way to solve it easily? Here is an example:

A 3 uC charge is at the origin, a -5 uC charge is at +0.2 m. Find the location of an +8 uC charge so that the net force on the 8 uC charge is -7 N

We can place the 8 uC charge on the negative side say at x m from the origin.

Then we can find the net force on 8 uC and then set it to - 7 N.

This is what I am getting.

-3 /x^2 + 5/(x+0.2)^2 = - 97.2

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# Tedious Algebra- Is it needed? - Coulomb Force

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