Question

Two positive charges of magnitude q each are placed at the ends of a 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 :

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

Answer 1

Answer: (A)

$\frac{1}{4\pi {ϵ}_0}\frac{2qQ}{a}(1-\frac{1}{\sqrt{5}})$

$U_i=\frac{2kqQ}{a}+\frac{2k(-q)Q}{\sqrt{5}a}=\frac{1}{4\pi {ϵ}_0}\cdot \frac{2qQ}{a}[1-\frac{1}{\sqrt{5}}]$

$U_f=0$

By conservation of energy

Gain in $KE=$ loss in PE

$K=\frac{1}{4\pi {ϵ}_0}\cdot \frac{2qQ}{a}[1-\frac{1}{\sqrt{5}}]$