17 (a) an infinitely long positively charged straight wire has a linear charge density of lamda cm(inverse). and electron is revolving around the wire as its centre with a constant velocity in a circular plane perpendicular to the wire. deduce the expression for its kinetic energy.

(b) plot a graph of the kinetic energy as a function of charge density lamda.

 ELECTRIC FIELD due to the infinitely long positively charged wire,

E=λ/2π ε0 r                

also the centripetal force required by the electron to revolve is given by

F1=(mv^2)/r                    (1)

the electrostatic force of attraction between the electron and wire

F2=eE

F2=eλ/2π ε0 r                 (2)

now,

equate 1 and 2 and try to get an expression for kinetic energy in terms of (mv^2)/2

the plot should be a straight line as both the quantities are directly proportional to each other