Unknown Charge Ratio Calculation

[jlwood13]

Homework Statement

You are given two unknown point charges, Q_1 and Q_2 . At a point on the line joining them, one-third of the way from Q_1 to Q_2 , the electric field is zero (see figure). The charges are separated by length, L.

What is the ratio of the charges Q₁/Q₂?

Homework Equations

F=k(Q₁Q₂)/r²

The Attempt at a Solution

I tried to put one charge in terms of the other, but I got lost and it seemed to be going nowhere. I'm stuck..

 

[kuruman]

We cannot see the figure pending approval. What is the question? Do you know the separation between the charges?

In any case, you will need to say that the sum of the electric fields generated by the two charges at the given point is zero. Remember that electric fields are vectors, so what must be true for these two vectors to add up to zero?

 

[jlwood13]

I apologize. I added the relevant question.. If they add up to zero, they must be opposite in direction and proportional, correct?

 

[jlwood13]

I figured it out. Using E=kQ/r^2, set kQ1/(r1)^2=kQ2/(r2)^2 and solve for Q1/Q2. r1=l/3, r2=2l/3. Thanks for your help.