**1. The problem statement, all variables and given/known data**

Three point charges, q1, q2 and q3 all on x-axis (i.e y=0 and z=0)

+q1 at x = 0

-q2 at dist from origin x = a

+q3 at dist from origin x = -2a

where q1, q2 and q3 are magnitudes of the charges.

Assuming q1 = q2 derive magnitude of q3 in order for there to be zero net force on q1.

**2. Relevant equations**

Coulombs law

F_{12} = (q1 * q2) / (r_{12})^{2} rhat_{12}

**3. The attempt at a solution**

attempt 1

in order for there to be no force on q1 then,

-q2(a) = q3(2a)

so

q3 = (-q2*a)/2a = -q2/a

bit too simplistic?

or attempt 2

F_{12} = 1/4*∏*ε_{0} * (q1*q2) / (r_{12})^{2} rhat_{12} .

F_{12} = 1/4*∏*ε_{0} * (q1*q2) / (a^{2}) **e**_{x}

F_{13} = 1/4*∏*ε_{0} * (q1*q3) / (r_{13})^{2} * rhat_{12}

F_{13} = 1/4*∏*ε_{0} * (q1*q3) / (-2a^{2}) **-e**_{x}

Resultant

magnitude F_{1} = 0 = 1/4*∏*ε_{0} * ((q1*q2) / (a^{2}) **e**_{x} + (q1*q3) / (-2a^{2}) **-e**_{x}

agh, run out of input time, will be back

Am I on the right track?

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