JEE PYQ: Electrostatics Question 27
Question 27 - 2020 (06 Sep Shift 2)
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 $x$-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:
(1) $\frac{P}{a}\sqrt{\frac{1}{\pi\varepsilon_0 ma}}$
(2) $\frac{P}{a}\sqrt{\frac{1}{2\pi\varepsilon_0 ma}}$
(3) $\frac{P}{a}\sqrt{\frac{2}{\pi\varepsilon_0 ma}}$
(4) $\frac{P}{a}\sqrt{\frac{2}{2\pi\varepsilon_0 ma}}$
Show Answer
Answer: (2)
Solution
Using energy conservation: $K_i + U_i = K_f + U_f$. $U_i = \frac{-2kp_1 p_2}{a^3}\cos(180°) = \frac{2kP^2}{a^3}$. $0 + \frac{2kP^2}{a^3} = \frac{1}{2}mv^2 + \frac{1}{2}mv^2 + 0$. $v = \sqrt{\frac{2kP^2}{ma^3}} = \frac{P}{a}\sqrt{\frac{1}{2\pi\varepsilon_0 ma}}$.
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