A long cylindrical volume contains a uniformly distributed charge of density ρ C m - 3 . The electric field inside the cylindrical volume at a distance x = 2 ε 0 ρ m from its axis is _____ V m - 1 .

Step-by-step solution

Given here, Volume charge density = ρ   C   m - 3 . Consider a Gaussian cylindrical surface of height h and radius x . Let q charge is enclosed by the cylinder of radius x . From Gauss's law, ∫ E d S cos 0 = q ε 0 Here, q = volume charge density × volume of imaginary cylinder. ⇒ E 2 π x h = ρ × π x 2 h ε 0 ⇒ E = ρ x 2 ε 0 ⇒ E = ρ 2 ε 0 × 2 ε 0 ρ = 1 Thus, electric field is 1   V   m - 1 .