Question

Two identical electric point dipoles have dipole moments $\vec{P}_{1}=P \hat{i} $ and $\vec{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 are infinitely far apart is :

• A. $\frac{ p }{ a } \sqrt{\frac{1}{\pi \varepsilon_{0} ma }}$
• B. $ \frac{ p }{ a } \sqrt{\frac{3}{2 \pi \varepsilon_{0} ma }}$
• C. $\frac{ p }{ a } \sqrt{\frac{1}{2 \pi \varepsilon_{0} ma }}$
• D. $ \frac{ p }{ a } \sqrt{\frac{2}{\pi \varepsilon_{0} ma }}$

Answer 1

Answer: (C)

Using energy conservation:
$KE _{i}+ PE _{ i }= KE _{ f }+ PE _{ f }$

$O +\frac{2 KP }{ a ^{3}} \times P =\frac{1}{2} mv ^{2} \times 2+0$
$V =\sqrt{\frac{2 P ^{2}}{4 \pi \varepsilon_{0} a ^{3} m }}=\frac{ P }{ a } \sqrt{\frac{1}{2 \pi \varepsilon_{0} am }}$