A long cylindrical wire carries a positive charge of linear density 2.0 × 10–6 C m–1. An electron revolves around it in a circular path under the influence of the attractive electrostatic force. Find the kinetic energy of the electron. Note that it is independent of the radius.


Given:


Linear charge density of wire=2.0× 10-6C=λ


We know that,


Electric field E due to a linear charge distribution of linear charge density λ at a distance r from the line is given by


….(i)


Now,


Magnitude of Force experienced by a charge q in an electric field of intensity E is given by



Here the charge particle is electron so the charge =q=e


Since this electron revolves around the wire in a circular path under the influence of this electrostatic force this force is equal to the centripetal force experienced by the electron


∴ …(ii)


Where,


m=mass of electron=9.1× 10-31kg


r=radius of orbit in which electron revolves


q=e=charge of electron=1.6× 10-19C


E=electric field due to line charge


V=velocity of electron


We know that ,


Kinetic energy of electron is given by


…(iii)


Where,


m=mass of electron


v=velocity of electron


from eqn,(ii) ,



Therefore kinetic energy of electron is given by



Putting value of E from eqn.(i)




Thus kinetic energy is independent of radius(r)


⇒ J


⇒ J


Therefore kinetic energy of electron while revolving around a cylindrical charge is given by 2.88× 10-17J and it is independent of radius.


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