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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 \frac{P}{a}\sqrt{\frac{1}{\pi \epsilon _{0}ma}}
 
Option: 2 \frac{P}{a}\sqrt{\frac{1}{2\pi \epsilon _{0}ma}}
Option: 3 \frac{P}{a}\sqrt{\frac{2}{\pi \epsilon _{0}ma}}  
Option: 4 \frac{P}{a}\sqrt{\frac{3}{2\pi \epsilon _{0}ma}}

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\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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Deependra Verma

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