Electric field in a region is given as `hatE=(10-5x)hati`. A charge particle of mass `5kg` and charge `Q(=1C)` is situated at origin and free to move given electric field. Then choose the correct options (Neglect gravity):

Options

A. Motion of charge particle is Oscillatory
B. Maximum displacement of charge particle from origin is `4SI` units
C. Maximum velocity gain by charge particle is `2 SI` units
D. The position of charge particle, when velocity gained by particle is maximum, is `2 SI` units

Answer

A, B, C, D

Explanation

`vecE=(10-5x)i`
`m=5kg`
`vecF=qvecE`
`vecf=(10-5x)i`
(a) `Fprop-x`
so motion of charge particle oscillatory (b) `F=0` at `x=2`
oscillation about `x=2`
so maximum displacement is 4
`F=10-5x`
`=a=(10-5x)/2`
`a=2-x`
`a=-(x-2)`
so `w^(2)=1`
`w=1`
(c) `v_("max")=Aw`
`A=2`
(d) velocity at mean position at `x=2`