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Two identical electric point dipoles have dipole moments p₁ = p î and p₂ = −p î 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:

1. (1) (p)/(a)√((1)/(πε₀ m a))
2. (2) (p)/(a)√((3)/(2πε₀ m a))
3. (3) (p)/(a)√((1)/(2πε₀ m a))
4. (4) (p)/(a)√((2)/(πε₀ m a))

Correct answer: (3) (p)/(a)√((1)/(2πε₀ m a))

Solution

For collinear dipoles U = (1/4*pi*e0)*(2p^2/a^3). All of this converts to KE = m v^2 (both masses), giving v^2 = p^2/(2*pi*e0*m*a^3), so v = (p/a)*sqrt(1/(2*pi*e0*m*a)).

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