Question 85 of 311

A point charge of $10µC$ is placed at the origin. At what location on the $X$-axis should a point charge of $40µC$ be placed so that the net electric field is zero at $x=2cm$ on the $X$-axis ?

A$x=6cm$B$x=4cm$C$x=8cm$D$x=–4cm$

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Answer: (A) $x=6cm$

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 $0$,
${E}_{P}=0 \Rightarrow \dfrac{k\times 10}{{2}^{2}}=\dfrac{k\times 40}{{\left({X}_{0}-2\right)}^{2}}$
$\Rightarrow \dfrac{1}{2}=\dfrac{2}{{X}_{0}-2}$
$\Rightarrow {X}_{0}-2=4$
Therefore, the charge is located at ${X}_{0}=4+2=6cm$