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 $m = 12\, g$ 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)

$\left|F_{1}\right|=\left|\frac{9\times10^{9}\times\left(-4\right)\times8\times10^{-12}}{\left(2\right)^{2}}\right|=72\times10^{-3}\,N$
$\left|F_{2}\right|=\frac{9\times10^{9}\times8\times8\times10^{-12}}{\left(2\right)^{2}}=144\times10^{-3}\,N$

$f_{y}=F_{1}\,sin30^{°}+F_{2}\,sin30^{°}=108\times10^{-3}\,N$
$f_{x}=F_{2}\,cos30^{°}-F_{1}\,sin30^{°}=36\sqrt{3}\times10^{-3}\,N$
$F=f_{x}\,\hat{i}+f_{y}\,\hat{j}$ or $\vec{F}=36\sqrt{3}\times10^{-3}\,\hat{i}+108\times10^{-3}\,\hat{j}$
$m=12\,g=12\times10^{-3}\,kg$
$\vec{a}=\frac{\vec{F}}{m}$
$=\frac{\left(36\sqrt{3}\hat{i}+108\hat{j}\right)\times10^{-3}}{12\times10^{-3}}$
$=3\sqrt{3}\,\hat{i}+9\,\hat{j}$