Two identical electric point dipoles have dipole moments \(\overrightarrow{p}_{1}= p\hat i\) and \(\overrightarrow{p}_{2}=- p\hat i\) and are held on the \(x-\)axis at distance \('a'\) from each other. When released, they move along the \(x-\)axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is \('m',\) their speed when they arc infinitely far apart is

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Answer & Solution

Correct Answer

(C) \(\frac{ p }{ a } \sqrt{\frac{1}{2 \pi \varepsilon_{0} ma }}\)

Detailed explanation

Using energy conservation

\(KE _{ i }+ PE _{ i }= KE _{ f }+ PE _{ f }\)

\(O +\frac{2 KP }{ a ^{3}} \times P =\frac{1}{2} mv ^{2} \times 2+0\)

\(V =\sqrt{\frac{2 P ^{2}}{4 \pi \varepsilon_{0} a ^{3} m }}=\frac{ P }{ a } \sqrt{\frac{1}{2 \pi \varepsilon_{0} am }}\)

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