An infinite line charge produces a field of $9 imes 10^4$ N/C at a distance of 2 cm. The linear charge densi

Question

An infinite line charge produces a field of $9 	imes 10^4$ N/C at a distance of 2 cm. The linear charge density is:

Accepted Answer

The electric field $E$ produced by an infinite line charge with linear charge density $\lambda$ at a distance $r$ is given by $E = \frac{\lambda}{2\pi\varepsilon_0 r}$. 
Rearranging for $\lambda$: $\lambda = E(2\pi\varepsilon_0 r) = \frac{E \cdot r}{2k}$ where $k = \frac{1}{4\pi\varepsilon_0} = 9 	imes 10^9$ N m$^2$ C$^{-2}$.
Given:
$E = 9 	imes 10^4$ N/C
$r = 2$ cm $= 0.02$ m

Calculation:
$\lambda = \frac{(9 	imes 10^4) 	imes 0.02}{2 	imes (9 	imes 10^9)}$
$\lambda = \frac{1.8 	imes 10^3}{18 	imes 10^9} = 0.1 	imes 10^{-6}$ C/m
$\lambda = 0.1 \, \mu$C/m.
(See NCERT Physics Class 12, Exercise 1.23).

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