Question

Two identical coaxial rings each of radius R are separated by a distance of $\sqrt{3}R$, They are uniformly charged with charges +Q and -Q respectively. The minimum kinetic energy with which a charged particle (charge + q) should be projected from the center of the negatively charged ring along the axis of the rings such that it reaches the center of the positively charged ring is :

• A. $\frac{Qq}{4\pi {\epsilon }_{0}R}$
• B. $\frac{Qq}{2\pi {\epsilon }_{0}R}$
• C. $\frac{Qq}{8\pi {\epsilon }_{0}R}$
• D. $\frac{3Qq}{4\pi {\epsilon }_{0}R}$

Answer 1

The correct option is A $\frac{Qq}{4\pi {\epsilon }_{0}R}$

Use energy conservation,

$U_i=U_f$

$\frac{1}{2}m{v}^2+\frac{KQq}{\sqrt{({\sqrt{3R}}^2+R^2)}}+\frac{K(-Q)q}{\sqrt{{\sqrt{0}}^2+R^2}}=\frac{KQq}{\sqrt{({\sqrt{0}}^2+R^2)}}+\frac{K(-Q)q}{\sqrt{({\sqrt{3R}}^2+R^2)}}$

$\Rightarrow \frac{1}{2}m{v}^2=\frac{KQq}{R}$