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Two identical electric point dipoles hav...

Two identical electric point dipoles have dipole moments `vec(P_1) = p hati and vec(P_2) = p hati` and are held on the x axis at distance 'a' from each other. When released, they move along the x-axis with the direaction of their dipole moments remaining unchanged. If the mass of each dipole is 'm', their speed when they are infinitely for apart is :

A

`(p)/(a)sqrt((1)/(piepsilon_(0)ma))`

B

`(p)/(a)sqrt((1)/(2piepsilon_(0)ma))`

C

`(p)/(a)sqrt((2)/(piepsilon_(0)ma))`

D

`(p)/(a)sqrt((3)/(2piepsilon_(0)ma))`

Text Solution

Verified by Experts

The correct Answer is:
B

By energy conservation
`k_(i)+u_(i)=k_(f)+u_(f)`
`0-(2k.p_(1))/(r^(3))p_(2).cos(180^(@))=(1)/(2)mv^(2)+(1)/(2)mv^(2)+0`
`mv^(2)=(2kp_(1)p_(2))/(r^(3))`
`implies v=sqrt((2kp_(1)p_(2))/(mr^(3)))`
`p_(1)=p_(2)=p and r=a`
`v=(p)/(a)sqrt((1)/(2piepsilon_(0)ma))`
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