An infinite line charge produces an electric field of 1 . 8 × 10 5 N C - 1 at a distance of 2 cm . Calculate the linear charge density.

Given, The electric field produced by the infinite linear charge E = 1 . 8 × 10 5 N C - 1 Distance at which electric field is calculated d = 2 cm = 2 × 10 - 2 m Electric field due to infinite linear charge at a distance d from it is E = λ 2 π ε ∘ d ⇒ λ = 2 π ε ∘ E d = 4 π ε ∘ E d 2 = 18 × 10 4 × 0 . 02 9 × 10 9 × 2 = 0 . 02 × 10 - 5 C m - 1 = 0 . 2 μ C m - 1 Hence, the linear charge density is 0 . 2 μ C m - 1 .

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