Two identical electric point dipoles have dipole moments p₁ = pi and… | JEE Main 2020 (6 Sep, Shift 2)

Q60JEE Main 2020 · 6 SEP · SHIFT 2Difficult

Electric Dipole

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:

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Answer: (c)

Coaxial dipoles: $U = -\vec p_2\cdot\vec E_1 = -(-p)\frac{2kp}{a^3} = \frac{2kp^2}{a^3}$ (positive, so they repel).
By symmetry both move with the same speed: $2\cdot\frac12 mv^2 = \frac{2kp^2}{a^3}$
$v^2 = \frac{2p^2}{4\pi\epsilon_0 ma^3} = \frac{p^2}{2\pi\epsilon_0 ma^3}$
$v = \frac{p}{a}\sqrt{\frac{1}{2\pi\epsilon_0 ma}}$ , so the answer is (c).

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