Question

An infinitely long positively charged straight wire has a linear charge density λ. An electron is revolving in a circle with a constant speed v such that the wire passes through the centre, and is perpendicular to the plane, of the circle. Find the kinetic energy of the electron in terms of the magnitudes of its charge and linear charge density λ on the wire.

Answer 1

Infinitely long charged wire produces a radial electric field.

E = `lambda/(2piε_0r)` .............(i)

The revolving electron experiences an electrostatic force and provides the necessary centripetal force.

∴ eE = `(mv^2)/r` ...............(ii)

⇒ `(e.lambda)/(2piε_0r) = (mv^2)/r ⇒ mv^2 = (elambda)/(2piε_0)`

The kinetic energy of the electron,

K = `1/2mv^2 = (elambda)/(4piε_0)`