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. $\frac{ Q }{2 \pi \varepsilon_{0}}\left[\frac{1}{ a }+\frac{1}{\sqrt{ s ^{2}+ a ^{2}}}\right]$
• B. $\frac{ Q }{4 \pi \varepsilon_{0}}\left[\frac{1}{ a }+\frac{1}{\sqrt{ s ^{2}+ a ^{2}}}\right]$
• C. $\frac{ Q }{4 \pi \varepsilon_{0}}\left[\frac{1}{ a }-\frac{1}{\sqrt{ s ^{2}+ a ^{2}}}\right]$
• D. $\frac{ Q }{2 \pi \varepsilon_{0}}\left[\frac{1}{ a }-\frac{1}{\sqrt{ s ^{2}+ a ^{2}}}\right]$

Answer 1

Answer: (D)

$V _{ A }=\frac{ KQ }{ a }-\frac{ KQ }{\sqrt{ a ^{2}+ s ^{2}}}$
$V _{ B }=\frac{- KQ }{ a }+\frac{ KQ }{\sqrt{ a ^{2}+ s ^{2}}}$
$V _{ A }- V _{ B }=\frac{2 KQ }{ a }-\frac{2 KQ }{\sqrt{ a ^{2}+ s ^{2}}}$
$=\frac{ Q }{2 \pi \varepsilon_{0}}\left(\frac{1}{ a }-\frac{1}{ s ^{2}+ a ^{2}}\right)$