An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density + σ . The electron at t = 0 is at a distance of 1 m from S and has a speed of 1 m s - 1 . The maximum value of σ , if the electron strikes S at t = 1 s is α m ϵ 0 e C m 2 . The value of α is _____.

Step-by-step solution

The value of the electric field due to the uniformly charged plane sheet is given by E = σ 2 ε 0 . . . 1 Thus, the force on the electron is given by F = - e E = - σ e 2 ε 0 . . . 2 So, the acceleration of the electron is given by a = - σ e 2 ε 0 m Given, u = 1 m s - 1 , t = 1 s and S = - 1 m Using the equation of motion, it can be written that - 1 = 1 × 1 - 1 2 × σ e 2 ε 0 m × ( 1 ) 2 ⇒ σ = 8 ε 0 m e C m - 2 ∴ α = 8 .