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Question
An infinite line charge produces a field of 9 × 104 N/C at a distance of 2 cm. Calculate the linear charge density.
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Solution
The electric field produced by the infinite line charges at a distance d having linear charge density λ is given by the relation,
E = `lambda/(2 pi in_0"d")`
λ = `2 pi in_0"dE"`
Where,
d = 2 cm = 0.02 m
E = 9 × 104 N/C
∈0 = Permittivity of free space
`1/(4 pi in_0)` = 9 × 109 N m2 C−2
λ = `(0.02 xx 9 xx 10^4)/(2 xx 9 xx 10^9)`
λ = 10−7 C/m
λ = 0.1 × 10−6 C/m
λ = 0.1 μC/m
Therefore, the linear charge density is 0.1 μC/m.
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