Solve Columns Law Problem: Magnitude of 3rd Charge

[iamtrojan3]

Homework Statement

Take three charged objects and place them on the x-axis. The first charge is + 11 microC, and is placed at +0.85 m. The second charge is -4.6 microC, and is placed at -0.22 m. The third charge is placed at the origin. If the net force on the third charge has a magnitude of 6.0(10-4) N, what is the magnitude of the charge?

Homework Equations

F=k (q1q2)/r^2

The Attempt at a Solution

i can find each charge magnitude in respect to the 3rd charge with the equation, but don't no where to go from there.
Thanks

 

[Doc Al]

Show exactly what you did. Hint: Call the unknown charge Q. Use Coulomb's law to solve for the force exerted on that charge by each of the other two charges.

 

[iamtrojan3]

ok i got my answer but I am not sure if its right.
basically i added 2 of coulombs equations 2gether.
6E-4= K(4.6xq2)/(0.22^2)+ K(11xq2)/(0.85^2)
after some algebra
6E-4=8.5E11q2+1.37E11q2
Factor out q2
q2= 6E-4/9.87E11
i got q2 to be around 6E-16 Micro C which = 6E-10 C
the answer is suppose to be "6.1E-10C". It might rounding error or i might be wayyyy off.
Can someone please check this?
Thanks

 

[Doc Al]

ok i got my answer but I am not sure if its right.
basically i added 2 of coulombs equations 2gether.
6E-4= K(4.6xq2)/(0.22^2)+ K(11xq2)/(0.85^2)

The charges are in microC, so they should be 4.6E-6 & 11E-6 C in this equation. That should explain why your answer is so far off.

 

[iamtrojan3]

yes, but is my train of thought even close to what your suppose to do?

 

[Doc Al]

Your method is perfectly correct. Fix those charge values and you should get the right answer.