# Determine a point where the electric field is zero

Q1 = 0.000004 d1 = -0.01 m
Q2 = -0.000001 d2 = 0.03 m

Now using that information, I found that the electric field at x = 0.0 m is 3.7 x 10^8 N/C

now i need to find out at which point the electric field is zero.

I made a program to guess and check for me, and what I do is:

[k * 0.000004] / (x+d1)^2 = field 1
[k * -0.00001] / (x-d2)^2 = field 2

then field 1 - field 2 = net electric field at x

The calculations are not wrong because when i enter 0, i get the correct answer, and when i plug in other numbers (1, 4, 5) that i have worked out, it gives me the correct answer also.

My problem is that it seems that there will never be an electric field of zero, it just gets smaller and smaller.

For example, at a point of 1 million meters, the net electrical field is 4.493999982024E-08

at a point of 100 million meters, the net electrical field is 4.4939999998202E-12

so it just gets smaller and smaller, but will it ever get to zero? or am i doing somethign wrong?

Thanks

Doc Al
Mentor
While it's certainly true that the field goes to zero at infinity, I don't think that's what they are looking for.

Forget computer programs. Instead, figure out the formula for the total field at any point. Note that signs matter! You may want to break up the x-axis into three regions ( < d1; d1 to d2; > d2) and consider the field in each region separately. Give it a try.

well that formula would be:

(x is in cm)

(N/C) = {(k * 0.000004) / [(x+1)^2 / 100]} - {(k * 0.000001) / [(x-3)^2 / 100]}

so i know that i would set n/c to zero, but where do i go from there?

Doc Al
Mentor
Since the sign of the fields from each charge changes from one region to the other, you'll need a separate formula for the field in each region. (For example: the field from a + charge is negative on one side, positive on the other.)