Question

An object with a charge of +6.5 µC is placed at the origin and an object with a charge of -3.2 µC is placed at x = 25 cm. Where along the x axis can another charged object be placed so that it will experimence no net force? (Hint: since F=Eq, there is no electrostatic force where there is no electrostatic field.)

Answer 1

\[\sum_{1}^{2}E=0\]
implies \[E_1+E_2=0\]
E=kq/d^2
\[k \left\{ \left( q1/(Xp-X1)^2 \right)+q_2/(Xp-X2)^2 \right\}=0\]

you have to solve this equation where
k = u can simplify
q1=6.5 10^-6 C
q2=-3.2 10^-6 C
Xp is you're looking for
X1=0
X2=25 10^-2 m

The results is likely this: (more than 25 for sure)