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Question

Two identical rings of radii 0.1 m are placed co-axially at a distance 0.5 m apart. The charges on the rings are 2μC and 4μC respectively. The work done in transferring 5μC charge from the centre of one ring to that of the other will be nearest to :

A
0.50 J
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B
0.75 J
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C
1.00 J
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D
1.50 J
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Solution

The correct option is A 0.75 J
We know that the potential at a point on the axis of the ring due to the ring is V=14πϵ0qx2+R2
When charge Q=5μC at the center of 1st ring, the potential energy is
Ui=Q( potential due to 1st ring + potential due to 2nd ring )=Q[14πϵ0q102+R2+14πϵ0q2x2+R2]
When charge Q=5μC at the center of 2nd ring, the potential energy is
Uf=Q( potential due to 2 nd ring + potential due to 1st ring )=Q[14πϵ0q202+R2+14πϵ0q1x2+R2]
Work done , W=ΔU=UfUi=Q4πϵ0[q2Rq1R+q1x2+R2q2x2+R2]
or W=(9×109)×5×106[4×1060.12×1060.1+2×1060.52+0.124×1060.52+0.12]
=0.72J

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