A long cylindrical wire carries a positive charge of linear density `2.0 xx 10^(-8) C m^(-1)`. An electron revolves around it in a circular path under the influence of the attactive electrostatic force. Find the kinetic energy of the electron. Note that it is independent of the radius.

Answer

`2.88xx10^(-17) J`

Explanation

Due to a line charge,
`E = (lambda)/(2pi in_(0) r) = (2 lambda)/(4pi in_(0) r)`
Force exerted by this field on electron
`F = qE = (e. 2 lambda)/(4pi in_(0) r)`
Force exerted by Electric field = Cenptripetal force
`F = (mv^(2))/(r )`
or `(e. 2 lambda)/(4pi in_(0) r) = (mv^(2))/(r )`
So `v^(2) = (e. 2 lambda)/(4pi in_(0) m)`
`K.E. = (1)/(2) mv^(2) = (1)/(2) m ((e.2 lambda)/(4pi in_(0) m)) = (e lambda)/(4 pi in_(0))`
`= 9xx10^(9) xx1.6xx10^(-9) xx2xx10^(-8)`
`= 2.88xx10^(-17) J`