- #1

dock

## Main Question or Discussion Point

**[SOLVED] finding equilibrum point between two charges**

this is pure physics;ain't no theory development;so don't move me around.

assume you have two charges q

_{1}and q

_{2}on distance R.the problem i'll solve here is how to find the equilibrum point between those charges.

to do that you have to introduce new charge q

_{3}in the system and place it somewhere between the first two on the conecting line.assume that distance between q

_{1}and q

_{3}is x then:

F

_{13}x^2=-kq

_{1}q

_{3}

and

F

_{23}(R-x)^2=-kq

_{2}q

_{3}

but it also has to be

F

_{13}=-F

_{23}

this system of three equations gives the following:

-x^2q

_{2}=(R-x)^2q

_{1}

the solution for x is:

x

_{1}=(q

_{1}+sqrt(-q

_{1}q

_{2}))R/(q

_{2}+q

_{1})

x

_{2}=(q

_{1}-sqrt(-q

_{1}q

_{2}))R/(q

_{2}+q

_{1})

i wonder why if the charges are same by sing then x is some imaginary num and why if it is q

_{1}=-q

_{2}then x is infinite/undefined point?

am gratefull for your answers!!