A cylinder of large length carries a charge of 2 × 10 - 8 Cm - 1 . Find the electric field at a distance of 0 . 2 m from it.

Given, Linear charge density of the cylinder λ = 2 × 10 - 8 Cm - 1 Distance at which electric field is calculated d = 0 . 2 m Electric field due to infinite linear charge at a distance d from it is E = λ 2 π ε 0 d = 1 4 π ε 0 · 2 λ d = 9 × 10 9 × 2 × 2 × 10 - 8 0 . 2 = 4 . 495 × 10 19 NC - 1 m - 1

A cylinder of large length carries a charge of 2 × 10 - 8 Cm - 1 . Find the electric field at a distance of 0 . 2 m from it.

Given, Linear charge density of the cylinder λ = 2 × 10 - 8 Cm - 1 Distance at which electric field is calculated d = 0 . 2 m Electric field due to infinite linear charge at a distance d from it is E = λ 2 π ε 0 d = 1 4 π ε 0 · 2 λ d = 9 × 10 9 × 2 × 2 × 10 - 8 0 . 2 = 4 . 495 × 10 19 NC - 1 m - 1

An electron is revolving around a long line charge having charge density 2 × 10 − 8 C m − 1 . Find the kinetic energy of the electron, assuming that it is independent of the radius of electron's orbit.

Linear charge density of the line charge λ = 2 × 10 − 8 C m − 1 Electric field due to infinite linear charge at a distance d from it is E = λ 2 π ε 0 d Force acting on the electron revolving, m v 2 d = E e = λ e 2 π ε 0 d ⇒ 1 2 m v 2 = λ e 4 π ε 0 ⇒ Kinetic energy K = λ e 4 π ε 0 = 9 × 10 9 × 2 .0 × 10 − 8 × 1 .6 × 10 − 19 = 2 .88 × 10 − 17 J