Question

Two point charges lie along the y-axis. A charge of q1 = -7 μC is at y = 6.0 m, and a charge of q2 = -6.5 μC is at y = -4.0 m. Locate the point (other than infinity) at which the total electric field is zero.
I have no clue where to start so any information will be greatly appreciated!

Answer 1

Well, negative charges on either side of the x axis. So the E is in opposite directions between the charges, a likely place to find where they cancel (add to zero).
so set them equal
E1=E2 (they are in opposite directions)
k7e-6/(x+4)^2=k6.5e-6/(6-x)^2 this assumes x is on the right hand side. with that assumption, x should be positive.

7(6-x)^2=6.5(x+4)^2

take sqrt root of each side.
6-x=(x+4)sqrt(6.5/7)
let that last term be c
6-x-cx=4c
x(1+c)=6+4c
x= you do it. x is the position on the positive x side.
check my work.