# 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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