Finding where an electron is relative to a charge?

[Cathmore]

Homework Statement

25cm to the right of a 0.5 microcoulomb charge is a -1.2 microcoulomb charge. Where (relative to the 0.5 microcoulomb charge) would a free electron be if the net electric force on the electron is zero?

Homework Equations

Fe=kq1q1/r2
E=kq/r2

The Attempt at a Solution

I keep attempting to combine the equations F=kq1p/r2 with F=kq2p/r2, but obviously I keep ending up canceling out the r's, which doesn't exactly help me find the distance I'm looking for here. I could find the electric field for q1 compared to q2 and vice versa, but I can't see how that would help me with finding the electric field at the electron, since I don't know the distance of either point to the electron. I don't know the force between the electron and either charge, only that they cancel out, so I can't find distance that way. This seems like it should be a really simple question, but I'm so burnt out on summer classes! Help!

Edit: New attempt possibly solved it, I found E for both q1 to q2 and q2 to q1, added that to get the E for the electron, and used that with q2 to find the charge relative to q2. I subtracted that from the distance between q1 and q2 to get a distance that makes sense to me. (the electron is 0.0773m to the left of q1)

Am I right? Who knows. My brain is shutting down for the rest of the day.

 

[gneill]

A good place to start is to determine by inspection in which region the the electron should be located: to the left of the +charge, between the two charges, or to the right of the -charge. You should be able to determine this by estimating the directions of the force produced on the electron by the fixed charges; clearly if the net force is to be nil the forces induced by the two fixed charges must be in opposite directions (i.e. oppose each other).

Next, note that the radial distance from the electron to each charge is not the same. That is, a single variable "r" will not describe both without adding some value to one of them (what value would be appropriate?). You can use a single variable, r, if you add the appropriate value to r for one of the spans.