Given:

E = 9 × 10⁴ NC^-1

d = 2 cm

Let the linear charge density = λ Coulomb/metre

We know that, Electric field produced by a line charge with a linear charge density σ, at a distance d is given by,

…(1)

Where, λ = linear charge density.

ε₀ = permittivity of free space

ε₀ = 8.85 × 10^-12N^-1 m^-2C²

d = distance

From equation (1) we have,

⇒ λ = E × 2 × π × ε₀ × d

⇒ λ = 9 × 10⁴ NC^-1 × 2 × π × 8.85 × 10^-12N^-1 m^-2C² × 0.02m

⇒ λ = 10 μ Cm^-1

The linear charge density is 10 μ Cm^-1.