A positive point charge q is fixed at origin. A dipole with a dipole moment `vecp` is placed along the x-axis far away from the origin with `vecp` pointing along the positive x-axis.
Find the kinetic energy of the dipole when it reaches a distance d from the origin.

Options

A. `1/(4piepsilon_0)(pq)/(d^2)`
B. `1/(2piepsilon_0)(pq)/(d^2)`
C. ` 1/(2sqrt(2) pi epsilon_0) (dq)/d^2`
D. `(sqrt2)/(piepsilon_0) (dq)/(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))`