# Q 1.23: An infinite line charge produces a field of $9\times 10^{4}\frac{N}{C}$ at a distance of 2 cm. Calculate the linear charge density.

Given,

$\lambda = 9\times 10^{4}\frac{N}{C}$

d = 2 cm = 0.02 m

We know, For an infinite line charge having linear charge density $\lambda$, the electric field at a distance d is:

$E = k\lambda / d$

$\therefore 9\times10^4 = 9\times10^{9}\lambda / 0.02$

$\\ \implies \lambda = (9\times10^4\times0.02) /(2\times9\times10^{9}) = 10\times10^{-8} C/m = \\ 10\times10^{-6} C/cm = 10 \mu C/cm$

The linear charge density is $10 \mu C/cm$

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