Two identical electric point dipoles have dipole moments ⃗p₁=p̂i and ⃗p₂=-p̂i and are held on the x-axis at a distance a from each other. When released, they move along the x-axis with the directions of their dipole moments remaining unchanged. If the mass of each dipole is m, their speed when they…

Question

Two identical electric point dipoles have dipole moments ⃗p₁=p̂i and ⃗p₂=-p̂i and are held on the x-axis at a distance a from each other. When released, they move along the x-axis with the directions of their dipole moments remaining unchanged. If the mass of each dipole is m, their speed when they are infinitely far apart is

Accepted Answer

(2) p/a√1/(2πε₀ ma). For two dipoles separated by ⃗r=âi, U=1/(4πε₀ r³)[⃗p₁·⃗p₂-3(⃗p₁·̂r)(⃗p₂·̂r)]. Here ⃗p₁·⃗p₂=-p² and (⃗p₁·̂i)(⃗p₂·̂i)=(p)(-p)=-p², so U=1/(4πε₀ a³)[-p²+3p²]=(2p²)/(4πε₀ a³). U>0, so the pair repels; at infinity U=0 and all of it becomes kinetic energy shared by the two equal masses: 2×1/2mv²=U. mv²=(p²)/(2πε₀ a³)⇒ v²=(p²)/(2πε₀ m a³). v=p/a√1/(2πε₀ ma).

Step-by-step solution

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