Question

Two point charges $q_x=-4\mu C$ and $q_2=8\mu C$ are lying on the $y$-axis. They are equidistant from the point $P$, which lies on the $x$-axis. A small object of charge $q_0=8\mu C$ and mass $m=12g$ is placed at $P$.
When it is released, what is its acceleration in $m{s}^{-2}$ ?
(Neglect the effect of gravity)

• A. $3\sqrt{3}\hat{i}+9\hat{j}$
• B. $9\hat{i}+3\sqrt{3}\hat{j}$
• C. $3\hat{i}+3\sqrt{3}\hat{j}$
• D. $3\sqrt{3}\hat{i}+3\hat{j}$

Answer 1

Answer: (A)

$\left|F_1\right|=\left|\frac{9\times 10^9\times \left(-4\right)\times 8\times 10^{-12}}{{\left(2\right)}^2}\right|=72\times 10^{-3}N$
$\left|F_2\right|=\frac{9\times 10^9\times 8\times 8\times 10^{-12}}{{\left(2\right)}^2}=144\times 10^{-3}N$

$f_y=F_{1}sin30^{°}+F_{2}sin30^{°}=108\times 10^{-3}N$
$f_x=F_{2}cos30^{°}-F_{1}sin30^{°}=36\sqrt{3}\times 10^{-3}N$
$F=f_x\hat{i}+f_y\hat{j}$ or $\vec{F}=36\sqrt{3}\times 10^{-3}\hat{i}+108\times 10^{-3}\hat{j}$
$m=12g=12\times 10^{-3}kg$
$\vec{a}=\frac{\vec{F}}{m}$
$=\frac{\left(36\sqrt{3}\hat{i}+108\hat{j}\right)\times 10^{-3}}{12\times 10^{-3}}$
$=3\sqrt{3}\hat{i}+9\hat{j}$