# Electron at equilibrium, electrostatics. quick question

ok lets say i that theres two particles with charges Q1 and another with a charge Q2 and they are 5m away from eachother. if i wanted to find the location of an electron where it is at rest (or equilibrium) it can be to the left of q1, between q1 and q2, or to the right of q2.

heres what it would look like e1---------q1------------e2-------------… where e is an electron.
this shows where the electron could possibly be located. it will be one of the three of these

k now a question will be find the distance from q1.

if it were located at e1 then (Q1/r^2)=(Q2/(5-r)^2) (5 is the distance from q1-q2).

my question is, what would it be if it were located at e2 or e3?

my guess- e2- (q1/r^2)=(q2/r^2)
and for e3- (q1/r^2)=(q2/(5+r)^2)

whats the charge on q1 and q2 positive or negative? and are they of the same magnitude

well it could be anything... but like lets say that q1 has a charge of +5C and q2 has one of -2C, then it would be to the right of e3(possibly in the middle as well but lets just say to the right...). or if its q1=+4C and q2=+5C, then wouldnt it be in the middle. what would it be for these?

im just trying to find out if its (q1/(r^2))=(q2/???) for the middle and to the right of q2

For the first one where Q1=+5c and Q2=-2C i got R=both 13.6 m and 3.06m

im doin the next one now

for the next one i got both -42.3 and 2.36 but i belive that -42.36 is the correct one? am i right?

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i apologize for editing this like 5 times.