Charges +q and −q are placed at points A and B respectively which are at a distance 2L apart and C is the mid point between A and B. The workdone in moving a charge +Q along the semicircle CRD with B as centre is
A
qQ4πε0L
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B
qQ6πε0L
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C
qQ2πε0L
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D
−qQ6πε0L
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Solution
The correct option is D−qQ6πε0L
From the figure, we get
Potential at C=VC=0
Let, Potential at D=VD
VD=14πε0[q3L−qL]
=−2q4πε0[3L]
Potential difference between VD and VC is,
VD−VC=−2q4πε0(3L)−0=−q6πε0L
The workdone =Q[VD−VC]
=−qQ6πε0L
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Hence, (d) is the correct answer.