Two identical electric point dipoles have dipole moments P→1=Pi^ and P→2=-Pi^ 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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a
Pa 2π∈0ma
b
Pa 12π∈0ma
c
Pa 1π∈0ma
d
Pa 32π∈0ma
answer is B.
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Detailed Solution
Electric field at the location of 2nd dipole due to 1st dipole is E→1=14π∈o2Pa3i^So potential energy is U=-P→2.E→1 =14π∈o×2P2a3=P22π∈oa3When they will be infinitely far apart U= 0 and if final speed of each dipole is v , then kinetic energy is 12mv2+12mv2=mv2 Conservation of energy Kf-Ki=Ui-Uf ⇒mv2=P22π∈oa3 ⇒v=Pa×12π∈oma