Question

Three-point charges are arranged on a line. Charge q3 = +5.00 nC and is at the origin.
Charge q2 = -3.00 nC and is at x = +4.00 cm. Charge q1 is at x = +2.00 cm. What is
q1 (magnitude and sign) if the net force on q3 is zero?

Answer 1

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Draw down the forces,

   $F_{1,3}$  =  k$} q_{1} q_{3}$ / $r^2_{1,3}$

  $F_{2,3}$   =  k $q_{2} q_{3}$ / $r^2_{2,3}$

Notice that  $F _{2,3}$ points in the +x direction. So we need  $F_{1,3}$ to point in the −x direction, thus q1 must have a  positive charge. Next, we set the two forces equal:

 $F_{1,3}$  =  $F_{2,3}$

Solving for    $q_{1}$  given,

 k $} q_{1} q_{3}$ / $r^2_{1,3}$    =  k $q_{2} q_{3}$ / $r^2_{2,3}$

    $q_{1}$  /  $r^2_{1,3}$     =  $q_{2}$  / $r^2_{2,3}$    

            $q_{1}$       =   $q_{2} r^2_{1,3}$    / $r^2_{2,3}$

            $q_{1}$       =  (-3.00nC) $\frac{4 cm^2}{16cm^2}$

                    $q_{1}$  =0.750nC