Two thin wires rings each having a 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

$QR divided by 4 πε subscript 0 straight d squared$
$fraction numerator straight Q over denominator 2 πε subscript 0 end fraction open square brackets 1 over straight R minus fraction numerator 1 over denominator square root of straight R squared plus straight d squared end root end fraction close square brackets$

zero

$fraction numerator straight Q over denominator 4 πε subscript 0 end fraction open square brackets 1 over straight R minus fraction numerator 1 over denominator square root of straight R squared plus straight d squared end root end fraction close square brackets$

Solution

fraction numerator straight Q over denominator 2 πε subscript 0 end fraction open square brackets 1 over straight R minus fraction numerator 1 over denominator square root of straight R squared plus straight d squared end root end fraction close square brackets

straight v subscript 1 space equals space kq over straight R minus fraction numerator kq over denominator square root of straight R squared plus straight d squared end root end fraction straight v subscript 2 space equals space fraction numerator negative kq over denominator straight R end fraction plus fraction numerator kq over denominator square root of straight R squared plus straight d squared end root end fraction

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