A particle of mass `400 mg` and charged with `5 xx 10^(-9) C` is moving directly towards a fixed positive point charge of magnitude `10^(-8) C`. When it is at a distance of 10 cm from the fixed positive point charge it has a velocity of 50 cm/s. At what distance from the fixed point charge will the particle come momentarily to rest ? Is the acceleration constant during the motion ?

Explanation

If the particle comes to rest momentarily at a distance r from the fixed charge, then from conservation of energy' we have
`(1)/(2)m u^(2) + (1)/(4pi epsilon_(0)) (Qq)/(a) = (1)/(4pi epsilon_(0)) (Qq)/(r )`
Substituting the given data, we get
`(1)/(2) xx 40 xx 10^(-6) xx (1)/(2) xx (1)/(2)`
`= 9 xx 10^(9) xx 5 xx 10^(-8) xx 10^(-9)[(1)/(r ) - 10]`
or, `(1)/(r ) - 10 = (5 xx 10^(-6))/(9 xx 5 xx 10^(-8)) = (100)/(9) rArr (1)/(r ) = (190)/(9)`
`rArr r = (9)/(190)m`
or, i.e., `r = 4.7 xx 10^(-2)m`
As here, `F = (1)/(4pi epsilon_(0))(Qq)/(r^(2))`
so acc. `= (F)/(m) prop (1)/(r^(2))`
i.e., acceleration is not constant during the motion.