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# Two thin wire rings each having radius R are placed at a distance d apart with their axes coinciding . The charges on the two rings are +Q and -Q .The potential difference between the centres of the two rings is

$(a)\;zero\qquad(b)\;\large\frac{kQ}{d^2}\qquad(c)\;2kQ\;(\large\frac{1}{R}-\large\frac{1}{\sqrt{R^2+d^2}})\qquad(d)\;kQ(\large\frac{1}{R}-\large\frac{1}{\sqrt{R^2+d^2}})$

Answer : (c) $\;2kQ\;(\large\frac{1}{R}-\large\frac{1}{\sqrt{R^2+d^2}})$
Explanation :
Potential at O :
$V_{1}=\large\frac{kQ}{R}-\large\frac{kQ}{\sqrt{R^2+d^2}}$
Potential at $\;O_{1}\;:$
$V_{2}=\large\frac{kQ}{\sqrt{R^2+d^2}}-\large\frac{kQ}{R}$
$V_{1}-V_{2}=2kQ\;(\large\frac{1}{R}-\large\frac{1}{\sqrt{R^2+d^2}})\;.$