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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:
A, B, C, D
(a) Potential energy of the dipole-charge system
`U_i=0` (since the charge is far away)
`U_f=-Qxx(1)/(4piepsilon_0)(p)/(d^2)` [at a point (d, `omega`)
`:.` `K.E.=|U_f-U_i|=(1)/(4piepsilon_0)(pQ)/(d^2)`
(b) Electric field at origin due to dipole
`vecE=(1)/(4piepsilon_0)(2p)/(d^3)hati`
Thus, force on charge Q is given by
`vecF=QvecE=(2pQ)/(4piepsilon_0d^3)hati`
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