Two identical thin rings, each of radius R metres, are coaxially placed at a distance R metres apart. If Q1 coulomb and Q2 coulomb are respectively, the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of one ring to that of the other is
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a
zero
b
qQ1-Q2(2-1)/24πε0R
c
q2Q1+Q2/4πε0R
d
qQ1+Q2(2+1)/24πε0R
answer is B.
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Detailed Solution
VA=14π∈0Q1R+Q22R; VB=14π∈0Q2R+Q12RVA-VB=14π∈0RQ1+Q22-Q2-Q12 Work done =Q×V=q×VA-VB =q4π∈0RQ1+Q22-Q2-Q12 =q4π∈0R×122Q1+Q2-2Q2-Q1 =qQ1-Q2(2-1)24π∈0R