A point charge of 10 µ C is placed at the origin. At what location...

Let the charge $40\mu C$ be placed at a distance ${X}_{0}$ from the origin as shown in the figure.

For the electric field at $x = 2$ to be $0$,

${E}_{P} = 0 ⇒ \dfrac{k \times 10}{{2}^{2}} = \dfrac{k \times 40}{{\left({X}_{0} - 2\right)}^{2}}$

$⇒ \dfrac{1}{2} = \dfrac{2}{{X}_{0} - 2}$

$⇒ {X}_{0} - 2 = 4$

Therefore, the charge is located at ${X}_{0} = 4 + 2 = 6cm$