Q. 234.3( 38 Votes )
An infinite line charge produces a field of 9 × 104 N/C at a distance of 2 cm. Calculate the linear charge density.
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,
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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