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A charge +Q is fixed at the origin of th...

A charge `+Q` is fixed at the origin of the co-ordinate system while a small electric dipole of dipolement `vecp` pointing away from the charge along the x-axis is set free from a point far away from the origin.
(a) Calculate the K.E. of the dipole when it reaches to a point (d, 0).
(b) Calculate the force on the charge `+Q` at this moment.

Text Solution

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The correct Answer is:
(i) `KE=(qP)/(4pi in_(0) d^(2))` (ii) `vec(F)=(pq)/(2pi in_(0) d^(3)) hat(i)`
(i) Applying energy conservation principle, increase in kinetic energy of the dipole=decrease in electrostatic potential energy of the dipole.
`:.` KE of dipole at distance d from origin `= U_(1)-U_(f)`
`rArr KE = 0 - (vec(p).vec(E)) = vec(p).vec(E) = (phat(i)).((1)/(4pi epsilon_(0)).(q)/(d^(2))l) = (qp)/(4pi epsilon_(0) d^(2))`
(ii) Electronic field at origin due to the dipole.
`vec(E)=1/(4pi epsilon_(0))(2p)/d^(3)hat(i) (vec(E)_("axis") uarr uarr p)`
`:.` Force om charge q at distance d
`rArr vec(F)=qvec(E)=(pq)/(2pi epsilon_(0)d^(3))hat(i)`
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