You are given two unknown point charges, Q1 and Q2. At a point on the line joining them, one-third of the way from Q 1 to Q2, the electric field is zero. Are Q1 and Q2 like or unlike charges? How many times greater is Q2 than on Q1?

Question

I am really confused on this problem. Please help me set it up. Thanks.

Answer 1

Let x be the distance between Q1 and the point where the electric field is 0. Then the distance between Q2 and this point is 2x

E = 0 = k*Q1/x^2 + k*Q2 / (2x)^2
= k*Q1/x^2 +k*Q2 / 4x^2

or

k*Q1/x^2 = - k*Q2/4x^2

This can only happen if one of Q1 and Q2 is negative, and one is positive; also Q2 has to have a magnitude of 4 times Q1 to get the field to be 0 at this point