A particle with a specific charge `(alpha)` starts from rest in a region where the electric field has a constant direction, but whose magnitude increases linearly with time. The particle acquires a velocity v in time t.

Options

A. `v prop alpha`
B. `v prop sqrt(alpha)`
C. `v prop t`
D. `v prop t^(2)`

Answer

A, D

Explanation

Electric field `prop` (time (t))
E = kt
where k = Proportionality constant
acc. `(a) = (qE)/(m) = (q kt)/(m) = alpha kt`
where `alpha = q//m = ` specific charge.
`:. a = (dv)/(dt) = alpha kt `
`rArr int dv = int alpha kt dt`
`v = (1)/(2) alpha k t ^(2) rArr v = prop t^(2) and v prop alpha ` .