Electric field at distance r from the infinite line charge is E=k2λr
The necessary centripetal force to the point charge of mass m is provided by electrostatic attraction.
∴mv2r=qE=qk2λr or v=√2kλqm
The speed of charged particle is independent of orbital radius. Hence the K.E. of point charge in orbits of radius r and 2r is same. As the work done is the change of K.E, so the work done by all forces is zero.