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Question

Two short electric dipoles are placed as shown in figure.


The energy of electric interaction between these dipoles will be :

[Take k=14πε0]

A
2kp1p2cosθr3
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B
2kp1p2cosθr3
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C
2kp1p2sinθr3
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D
4kp1p2cosθr3
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Solution

The correct option is B 2kp1p2cosθr3
We know that for a very small change in potential dV, potential energy can be written as,
U=p1E

But for a dipole with dipole moment p2 we can write that,

E=2kp2cosθ^rr3+kp2sinθ^tr3

Since, dipole p1 is along the radial component of electric field

U=p1×(2kp2cosθr3)cos0

U=2kp1p2cosθr3

Hence, option (b) is the correct answer.

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