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Numerical

An infinite line charge produces a field of 9 × 10^{4 }N/C at a distance of 2 cm. Calculate the linear charge density.

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#### Solution

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

`"E" = lambda/(2piin_0"d")`

`lambda = 2piin_0"dE"`

Where,

d = 2 cm = 0.02 m

E = 9 × 10^{4} N/C

∈_{0} = Permittivity of free space

`1/(4piin_0)` = 9 × 10^{9} N m^{2} C^{−2}

`lambda = (0.02 xx 9 xx 10^4)/(2 xx 9 xx 10^9)`

= 10 μC/m

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

Concept: Electric Field - Electric Field Due to a System of Charges

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