Got challenged by teacher, Coulomb's Law.

[yasu7]

This may not be a challenge for some of you, but it is hard for me as I just got introduced to the topic, your help will be appreciated.
It is about Electric Force. Coulomb's Law.

Homework Statement

Charges of -1 micro coulomb and -4 microcoulomb are placed at opposite ends of a meter ruler. Where on the ruler could...
(a) a free electron be placed and be in electrostatic equilibrium?
(b) a free proton be placed and be in electrostatic equilibrium?

Homework Equations

F=K(q1q2)/r2

F= Force (Newtons)
Q= Coulombs charges
R= distance between the charges
K= botlzmann constant

The Attempt at a Solution

I tried getting the answer by doing math without involving phyisics, like this:If 4 microcolombs is 100%
then 1 microcoulomb might be 25%
and I have a 1 meter long ruler,
then the new coulomb would be placed 25% to the right from the force that has 1 microcoulomb. That would be 25 cms to the right from the -1 microcoulomb

I reach this conclusion by math logic, but I believe it's wrong and my teacher told me it really is wrong, my method is ambiguous so..

I hope someone helps me get me the correct answer.

 

[LowlyPion]

Welcome to PF.

You would be better served to set it up algebraically, where

X = distance to one charge and 1 - X = distance to the other.

Since you want the forces to be equal at that point ... then set them equal and solve for X.