A point charge of 10   µ C is placed at the origin. At what location on the X -axis should a point…

Let the charge $40 \mathrm{\mu C}$ be placed at a distance $X_0$ from the origin as shown in the figure.

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

$$\begin{gathered} E_P=0 \\ \Rightarrow \frac{k\times 10}{2^2}=\frac{k\times 40 }{{\left(X_0-2\right)}^2} \end{gathered}$$

$\Rightarrow \frac{1}{2}=\frac{2}{X_0-2}$

$\Rightarrow X_0-2=4$

Therefore, the charge is located at $X_0=4+2=6 \mathrm{cm}$