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I have two charges, q1 & q2, along a horizontal axis of length L. I supposed to determine the length at which another charge, Q, can be placed so that its net force is zero, other than infinitely away.

I'm using the equation:

F = kq1Q / r + kq2Q / r

-- > kq1Q / (L+x)^2 = -( kq2Q / x^2 ) where x is the distance the point is away from L.

I substitute my #s and I get the equation:

(8 / (l^2 + 2xL + x^2)) = -(2/x^2)

and then I get:

8x^2 = -2(L^2 + 2xL + x^2)

-4x^2 = L^2 + 2xL + x^2

0 = L^2 + 2xL + 5x^2

Is this right? I cannot seem to solve for x.

I thought I initially had it, but reworked through my math and realized I forgot to have 2q negative. What I initally got was:

L^2 + 2xL - 3x^2

I can solve that by 'unfoiling' easily, but, as I previously mentioned, the math isn't correct to get that equation.

Thank you for your help and have a wonderful day.

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# Homework Help: Coulomb's Law

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