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Q.

Two short electric dipoles are placed as shown. The energy of electric interaction between these dipoles will be:

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a

$\frac{2 {kP}_{1} P_{2} \cos θ}{r^{3}}$

b

$\frac{- 2 k P_{1} P_{2} \cos θ}{r^{3}}$

c

$\frac{2 {kP}_{1} P_{2} \sin θ}{r^{3}}$

d

$\frac{- 4 {kP}_{1} P_{2} \cos θ}{r^{3}}$

answer is B.

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Detailed Solution

$∵ U = - {\vec{P}}_{2} \cdot {\vec{E}}_{1}; \Rightarrow E_{1} \equiv \frac{2 kP}{r^{3}} \Rightarrow U = \frac{- 2 {kP}_{1} P_{2} \cos θ}{r^{3}}$

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