An indinitely long positively charged wire has a linear charge density `lambda cm^(-1)`. An electron is revolving around the wire as its center with a constant velocity in a circular plane perpendicular to the wire. Deduce the expression for KE of electron. Plot a graph of K.E as a function of charge density `lambda`.

Explanation

The electostatic force exerted by the infinitely long line charge provides the necessary centripetal force to the revolving electron.
`:. eE = (mv^(2))/(r ) , but E = (lambda)/(2pi in_(0) r)`
`(e lambda)/(2pi in_(0) r) = (mv^(2))/(r ) or v^(2) = (e lambda)/(2pi in_(0) m)`
`KE = (1)/(2) mv^(2) = (1)/(2) m ((e lambda)/(2pi in_(0) m)) = (e lambda)/(4pi in_(0))`
As KE `prop lambda`, therefore, graph of KE as a function of charge density will be a straight line as shown in Fig.