Net electrostatic force equals zero

[jmcoop75]

I am having trouble with this question and need some help please excuse any mispellings

the question deals with three charges q1 q2 and q3

q=1.2*10^-5

q1=+q or 1.2*10^-5
q2=-2q or -2.4*10^-5
q3=+3q or 3.6*10^-5

q1 and q3 are exactly .32 meters apart and I need to find what distance from q1 that q2 needs to be placed for the net electrostatic force on q2 to equal zero.

q1--------------------------q2-----------------------------q3
I---------------------------.32m----------------------------I

i know you need to set the magnitudes equal to each other

k=8.99*10^9

this is what I am coming up with please tell me if I am doing anything wrong

the first k is negative because it pulls to the left and is the weaker force while the second pulls to the right

-------q1----------q2---------------------q2---------q3
-k*(1.2*10^-5)(2.4*10^-5)/x^2 = k*(2.4*10^-5)*(3.6*10^-5)/(.32-x)^2

and then cancel the common terms

-k*q1/x^2 = k*q3/(.32-x)^2

I then understand that i need to take the squareroot of both sides and then solve for x but am confused about the exact process and continually come up with different answers.
I know that the correct answer is .12m but can't seem to get it.
any help is greatly apreciated.

 

[jbsteele]

Ok, so you are correct that you need to take the square root of both sides. After canceling out the common terms, you should have:-sqrt(kq1)/x = sqrt(kq3)/(.32-x)Now you can multiply both sides by x and (0.32 - x):-sqrt(kq1) = sqrt(kq3)x/(0.32 - x)Now move all the terms with x to one side:sqrt(kq3)x - sqrt(kq1)(0.32 - x) = 0Now factor to solve for x:x(sqrt(kq3) + sqrt(kq1)) = sqrt(kq1)*0.32So, finally, x = sqrt(kq1)*0.32 / (sqrt(kq3) + sqrt(kq1))Substituting in your values for k and q1 and q3, you will get the answer x = 0.12m. Hope this helps!