# 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 uchanged. If the mass of each dipole is 'm', their speed when they are infinitely far apart is : Option: 1   Option: 2 Option: 3   Option: 4

\begin{aligned} &\text { Using energy conservation: }\\ &\mathrm{KE}_{\mathrm{i}}+\mathrm{PE}_{\mathrm{i}}=\mathrm{KE}_{\mathrm{f}}+\mathrm{PE}_{\mathrm{f}} \end{aligned}

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

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