A long straight wire carries a charge with linear density `lamda`. A particle of mass m and a charge q is released at a distance r from the the wire. The speed of the particle as it crosses a point distance 2r is

Options

A. `sqrt((q lamda ln r)/(pi m in_(0)))`
B. `sqrt((q lamda ln2)/(pi m in_(0)))`
C. `sqrt((q lamda ln2)/(2 pi m in_(0)))`
D. `sqrt((q lamda ln2)/(pim in_(0)))`

Answer

B

Explanation

Work done by electric field `= q underset(r) overset(2r) (int) (2k lamda)/(r) dr`
`=q2 k lamda ln2`
`:. 2k lamda ln 2 =(1)/(2)mv^(2)`
`v= sqrt((4k lamda qln 2)/(m))=sqrt((lamda q ln 2)/(m piin_(0)))`.