Question

The two thin coaxial rings, each of radius '$a$ ' and having charges $+Q$ and $-Q$ respectively are separated by a distance of '$s$'. The potential difference between the centres of the two rings is :

• A. $\frac{Q}{2\pi {\epsilon }_0}\left[\frac{1}{a}+\frac{1}{\sqrt{s^2+a^2}}\right]$
• B. $\frac{Q}{4\pi {\epsilon }_0}\left[\frac{1}{a}+\frac{1}{\sqrt{s^2+a^2}}\right]$
• C. $\frac{Q}{4\pi {\epsilon }_0}\left[\frac{1}{a}-\frac{1}{\sqrt{s^2+a^2}}\right]$
• D. $\frac{Q}{2\pi {\epsilon }_0}\left[\frac{1}{a}-\frac{1}{\sqrt{s^2+a^2}}\right]$

Answer 1

Answer: (D)

$V_A=\frac{KQ}{a}-\frac{KQ}{\sqrt{a^2+s^2}}$
$V_B=\frac{-KQ}{a}+\frac{KQ}{\sqrt{a^2+s^2}}$
$V_A-V_B=\frac{2KQ}{a}-\frac{2KQ}{\sqrt{a^2+s^2}}$
$=\frac{Q}{2\pi {\epsilon }_0}\left(\frac{1}{a}-\frac{1}{s^2+a^2}\right)$