Two point charges q and q' are placed respectively at two points A and B. Let O be the midpoint of [AB]. Charge q placed at A creates at O an electric field of strength E=9×10^6 V/m. Determine the resultant electric field at O when:

Question

a) q'=q 
b) q'=-q

Answer 1

Let's see if I can explain why part b0 can't be solved.
Let's assume the charges are 2m apart so r is always 1. Now suppose I make q=1e-3 and q' = 0
E = kq/r^2 for each and half way the field is 9e6. So for part b) E = 18e6.
Now suppose I start with q = 2e-3 and q' = 1e-3. Again half way E = 9e6 as proscribed. But now for part b) E = 36e6. There's no one answer. In fact if I'm not mistaken there are infinite solutions.
Bob? That sound about right?