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Two thin circular rings of radius R each are kept on the same axis with their centres separated by a distance d. One ring carries charge +q and the other carries charge −q. What is the potential difference between the centres of the two rings?

1. (q)/(2πε₀) [(1)/(R)-(1)/(√(R²+d²)) ]
2. (qR)/(4πε₀ d²)
3. (q)/(4πε₀) [(1)/(R)-(1)/(√(R²+d²)) ]
4. zero

Correct answer: (q)/(2πε₀) [(1)/(R)-(1)/(√(R²+d²)) ]

Solution

V at centre of ring1 = (q/4 pi eps0)[1/R - 1/sqrt(R^2+d^2)] and centre of ring2 = its negative. Potential difference = (q/2 pi eps0)[1/R - 1/sqrt(R^2+d^2)].

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