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

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 ×10-8 Cm-1

The linear charge density is 10-7 Cm-1.

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