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

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.

Answers (1)
H Harsh Kankaria

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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