Question

Two positive charges of magnitude ${}^{\prime }{q}^{\prime }$ are placed at the ends of a side (side 1) of a square of side ${}^{\prime }2a^{\prime }$. 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 :

• A. zero
• B. $\frac{1}{4\pi {\epsilon }_0}\frac{2qQ}{a}\left(1+\frac{1}{\sqrt{5}}\right)$
• C. $\frac{1}{4\pi {\epsilon }_0}\frac{2qQ}{a}\left(1-\frac{2}{\sqrt{5}}\right)$
• D. $\frac{1}{4\pi {\epsilon }_0}\frac{2qQ}{a}\left(1-\frac{1}{\sqrt{5}}\right)$

Answer 1

Answer: (D)

Potential at point A,
$V_A=\frac{2kq}{a}-\frac{2ka}{a\sqrt{5}}$
Potential at point B,
$V_B=0$
$\therefore$ Using work energy theroem
$W_{AB)electric}=Q\left(V_A-V_B\right)$
$=\frac{2KqQ}{a}\left[1-\frac{1}{\sqrt{5}}\right]=\left(\frac{1}{4\pi {\epsilon }_0}\right)\frac{2Qq}{a}\left[1-\frac{1}{\sqrt{5}}\right]$