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Q.

Two identical thin rings, each of radius R metres, are coaxially placed at a distance of R metres from each other. If Q1 coulombs and Q2 coulombs are the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of first ring to that of the second is

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a

Zero

b

qQ1−Q2(2−1)/2×4πε0R

c

q2Q1+Q2/4πε0R

d

qQ1+Q2(2+1)/2×4π∈0R

answer is B.

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Detailed Solution

V1=kQ1R+kQ22RV2=kQ12R+kQ2RW=qV2−V1=kqQ2−Q11−12=14πε0(2−1)qQ2−Q12.
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Two identical thin rings, each of radius R metres, are coaxially placed at a distance of R metres from each other. If Q1 coulombs and Q2 coulombs are the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of first ring to that of the second is