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**Can you check this? -- Charges and Forces...**

## Homework Statement

A +3-mC charge and a -4-mC charge are fixed in position and separated by 5 meters.

A)Where could a +7-mC charge be placed so that the net force on it is zero?

B)Where could a -7-mC charge be placed so that the net force on it is zero?

I came up with this diagram:

|---------------5m------------------|

*----------------*------------------*

q[1] q[2] q[3]

|-------r[1]------|----------r[2]----|

## Homework Equations

F[1]=K(|q[1]*q[2]|)/r[1]^2

F[2]=K(|q[2]*q[3]|)/r[2]^2

r[1]+r[2]=5

k=8.99*10^9

|q[1]|=4

|q[3]|=3

|q[2]|=7

## The Attempt at a Solution

F[1]=F[2]<---Because they are equal

K(q[1]*q[2])/r[1]^2=K(q[3]*q[2])/(5-r[1])^2<---We get (5-r[1])=r[2] from r[1]+r[2]=5 solved for r[2])

Then after we solve for r[1] we get this:

r[1]=5*√(q[3])*(√(q[3])-√(q[

_{1}]))/(q[3]-q[1])

So that means that both the +7-mC charge and the -7-mC charge are in the same position. The number I got was r[1]=2.32m and r[2]=2.68m. Did I set this up, and execute this correctly?

Thank you very much for your time.