Q. Two positive charges of magnitude $'q'$ are placed at the ends of a side (side 1) of a square of side $'2a'$. Two negative charges of the same magnitude are kept at the other corners. Starting from rest, if a charge $Q$ moves from the middle of side $1$ to the centre of square, its kinetic energy at the centre of square is :
AIEEEAIEEE 2011Electrostatic Potential and Capacitance
Solution:
Potential at point A,
$V_{A} = \frac{2kq}{a}- \frac{2ka}{a\sqrt{5}}$
Potential at point B,
$V_{B} = 0$
$\therefore \quad$ Using work energy theroem
$W_{AB )\,electric} = Q\left(V_{A} - V_{B}\right)$
$=\quad \frac{2KqQ}{a}\left[1-\frac{1}{\sqrt{5}}\right]\quad\quad=\quad\left( \frac{1}{4\pi\varepsilon_{0}}\right) \frac{2Qq}{a}\left[1-\frac{1}{\sqrt{5}}\right]$
