An infinite line charge produces a field of 9 × 10⁴N/C at a distance of 2 cm. Calculate the linear charge density.

Electric field produced by the infinite line charges at a distance d ,having linear charge density λ  is given by the relation,

E =λ /2π ε₀ d

Therefore λ = 2π ε₀ dE

Where d= 2 cm=).02 m and E= 9 x 10⁴ N/C

ε₀ = Permittivity of free space and = 9 x 10⁹Nm²C⁻²

Therefore,

λ =   (0.02 x 9 x 10⁴)/(2x9x10⁹)

=10µC/m

Therefore, the linear charge density is 10µC/m.