(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A charge of +2q is placed at the origin and a second charge of -q is placed a x = 3cm. Where can a third charge +Q be placed so that it experiences a zero force?

2. Relevant equations

F=kQ1Q2/r^2

3. The attempt at a solution

OK I thought I had this until the roots of the quadratic I am solving come out to be imaginary...

Q1 = 2q

Q2 = -q

Q3 = +Q

I am assuming that Q3 must be placed to the right of Q2.

the distance between Q1 and Q3 = x+0.03m and the distance between Q2 and Q3 = x

If F on Q3 = 0 then FQ1=FQ2 at this point

F1on3 = k*Q1*Q3/r^2 = F 2on3 = k*Q2*Q3/r^2 ;; cancel k and Q3

Q1/r_{1to3}^{2}= Q2/r_{2to3}^{2}

Q1/(x+0.03m)^{2}=Q3/x^{2}

Q1*x^{2}= Q3*(x+0.03m)^{2}

2q*x^{2}/ -q = (x+0.03m)^{2}

-2x^{2}= (x+0.03m)^{2}

-2x^{2}= x^{2}+ 0.06x + 0.0009

0=3x^{2}+ 0.06x + 0.0009

Can anyone tell me where I've gone wrong here? Is my assumption that Q3 is to the right of Q2 incorrect?

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# Homework Help: Place a 3rd charge so net force is 0

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