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.

Options

A. `3/(4piepsilon_0)(pq)/(d^2)`
B. `3/(2piepsilon_0)(pq)/(d^2)`
C. `1/(2piepsilon_0)(pq)/(d^2)`
D. `1/(4piepsilon_0)(pq)/(d^2)`

Explanation

Conserving energy (fig)
`(-pE)_("initial")+(KE)_("initial")=` constant
or `0+0=-pxx(1)/(4piepsilon_(0))(q)/(q^(2))+KE`
or `KE=(pq)/(4piepsilon_(0)d^(2))`
`|F|=|(dU)/(dx)|=(pq)/(4piepsilon_(0))(d)/(dx)((1)/(x^(2)))`
`=(pq)/(4piepsilon_(0))(-2x^(-3))=(pq)/(2piepsilon_(0))(1)/(x^(3))`
Force on dipole `|F|=(1)/(2piepsilon_(0))(pq)/(d^(3))`