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Q.

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
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