A point charge of charge -q and mass m is released with negligible speed from a distance `sqrt(3) R` on the axis of a fixed uniformly charged ring of charge Q and radius R. Find out its velocity when it reaches it reaches at the centre of the ring.

Explanation

As potential due to uniformly charged ring at its axis (at x distance) is :
`V=(kQ)/sqrt(R^(2)+x^(2))` ,
So, potential at point a due to ring
`V_(1)=(kQ)/sqrt(R^(2)+3R^(2))=(kQ)/(2R)`
So potential energy of charge -q at point A
`P.E._(1)=(-kQq)/(2R)` and potential at point B, `V_(2)=(kQ)/R`
So, potential energy of charge -q at point `B : P.E._(2)=(-kQq)/R`
Now by energy conservation : `P.E._(1)+K.E._(1)=P.E._(2)+K.E_(2)`
`(-kQq)/(2R)+0=(-kQq)/R+1/2 mv^(2)" "implies" "v^(2)=(kQq)/(mR)`
So velocity of charge `-q` at point `B" "v=sqrt((kQq)/(mR))`