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Question

Two electric dipoles, A and B with respective dipole moments pA=4qa^i and pB=2qa^i are placed on the X axis with a separation R, as shown in the figure


The distance from A at which both of them produce the same potential is

A
R21
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B
2R21
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C
R2+1
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D
2R2+1
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Solution

The correct option is D 2R2+1
As, dipole moments of dipoles point in the same direction, potential of both dipoles can be same at some point between A and B. Let potentials be same at P, which is at distance x from B as shown below



Then , potential due to each dipole at P we get ,

4qa(Rx)2 = 2qa(x)2

2x2=(Rx)2

2x=Rxx=R2+1

Distance from A is

Rx=RR2+1=2R2+1

Hence, option (a) is the correct answer.

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