Browse Questions

# Two point charges $\;q_{1}=q_{2}=2\;\mu C\;$ are fixed at $\;x_{1}= +3m \;and\;x_{2}=-3m\;$ as shown in figure . A third particle of mass 1g and charge $\;q_{3}=-4\;\mu C\;$ are released from rest at $\;y=4m \;$. Find the speed of the particle as it reaches the origin .

$(a)\;12.4 \;m/s\qquad(b)\;6.2\; m/s\qquad(c)\;3.1\; m/s\qquad(d)\;None\;of\;these$

Answer : (b) $\;6.2 \;m/s$
Explanation :
$\bigtriangleup P\;.E=\large\frac{-2\times9\times10^{9}\times2\times4\times10^{-12}}{3} + \large\frac{2\times9\times10^9\times2\times4\times10^{-12}}{5}$
$\bigtriangleup P\;E=\large\frac{-144\times10^{-3}\times2}{3\times5}=\large\frac{-96\times10^{-3}}{5}$
Using conservation of total energy as their is no external force
$\bigtriangleup T\;.E=0$
$\bigtriangleup K\;.E + \bigtriangleup P\;.E=0$
$\large\frac{1}{2}\times1\times10^{-3}\times v^2=\large\frac{96\times10^{-3}}{5}$
$v=6.2\;m/s\;.$

edited Aug 13, 2014