A proton is fixed at origin. Another proton is released from rest, from a point at a distance `r` from origin. Taking charge of portion as e and mass as `m`, find the speed of the proton (i) at a distance `2r` from origin (ii) at large distance from origin.

Explanation

The proton moves away under electrostatic repulsion,
As there is no extemal force,
`W_("ext") = 0`
`rArr Delta`KE + `Delta`PE= 0
`rArr " ' ((1)/(2) mv^(2)) + (U_(f)- U_(i))= 0`
(i) `U_(f) = (e^(2))/(4 pi epsilon_(0)(2r)), U_(i) = (e^(2))/(4 pi epsilon_(0)(r))`
`rArr " " (1)/(2) mv^(2) = (e^(2))/(4 pi epsilon_(0)(2r))`
`rArr " " v = sqrt((e^(2))/(4 pi epsilon_(0)rm))`
(ii) `U_(f) = 0, U_(i) = (e^(2))/(4 pi epsilon_(0)r)`
`rArr " " (1)/(2) mv^(2) = (e^(2))/(4 pi epsilon_(0)r)`
`rArr " " v = sqrt( (2e^(2))/(4 pi epsilon_(0)rm))`