Net Electric Field of 2 charged particles fixed to X-axis

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To find the coordinate on the x-axis where the net electric field from two charged particles equals zero, the charges are q1 = 2.1*10^-8 C at x = 0.2m and q2 = -8.4*10^-8 C at x = 0.7m. The equation for the electric field, E = (8.99*10^9)q/r^2, is used, but the distances (r) from each charge to the point of interest must be treated separately. The confusion arises from equating the distances for both charges, which should not be the same; one distance must account for the separation between the two charges. Clarification is needed on how to set up the equation correctly to solve for the unknown distance.
Oaksmack
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2 Particles are fixed to an x-axis:
q1=2.1*10^-8 C @ x=.2m
q2=-4.00q1 @ x=.7m

We are trying to find the coordinate on the x-axis where the net electric field produced by the particles = 0.
The equation I have is

E=((8.99*10^9)q)/r^2

I got what i thought was q2 first, by multiplying 2.1*10^-8 by -4.00 to get -8.4*10^-8. From there I equated E1 & E2:
((8.99*10^9)(2.1*10^-8))/r^2 = ((8.99*10^9)(-8.4*10^-8))/r^2
from there, I had no idea how to solve for r.
I simplified the constant 8.99*10^9 with the respective q's, but just couldn't figure out how to solve for r without it canceling into 1 and having two numbers equaling each other. :confused:
Please help, I have a number of problems like this to do for this chapter.
 
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Almost correct except r in your equation
r is a distance from the charge you are considering. So each r on the left side and right side of your equation should not be equal. One should be include the distance between two point charges.
 
Wait, so one of the r's should be .5m, the distance between the two particles?
 
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