A long cylindrical wire carries a positive charge of linear density `lambda`. An electron `(-e ,m)` revolves around it in a circular path under the influence of the attractive electrostatic force. Find the speed of the electron.

Explanation

Electric field at perpendicular distance `r`
`E = (lambda)/(2 pi in_(0) r)`
The electric force on electron
`F = eE`
To move in circular path , necessary centripetal force is provided by electric force.
`F_(c ) = (mv^(2))/(r ) = eE = (e lambda)/(2 pi in_(0) r )`
`v = sqrt((e lambda)/(2 pi in_(0) m)) , v prop r^(0)`