An infinite line charge produces a field of 9 | vedclass

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Question

(A) Given:$E_1 = 9 	imes 10^4 	ext{ NC}^{-1}$$r_1 = 2 	ext{ cm}$$r_2 = 3 	ext{ cm}$The electric field $E$ due to an infinite line charge is given

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$6 	imes 10^4 	ext{ NC}^{-1}$

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(A) Given:$E_1 = 9 	imes 10^4 	ext{ NC}^{-1}$$r_1 = 2 	ext{ cm}$$r_2 = 3 	ext{ cm}$The electric field $E$ due to an infinite line charge is given by the formula:$E = \frac{\lambda}{2 \pi \varepsilon_0 r}$From this relation,we can see that $E \propto \frac{1}{r}$.Therefore,the ratio of the fields at two different distances is:$\frac{E_2}{E_1} = \frac{r_1}{r_2}$Substituting the given values:$\frac{E_2}{9 	imes 10^4} = \frac{2 	ext{ cm}}{3 	ext{ cm}}$Solving for $E_2$:$E_2 = \frac{9 	imes 10^4 	imes 2}{3}$$E_2 = 3 	imes 10^4 	imes 2$$E_2 = 6 	imes 10^4 	ext{ NC}^{-1}$Thus,the electric field at a distance of $3 	ext{ cm}$ is $6 	imes 10^4 	ext{ NC}^{-1}$.

An infinite line charge produces a field of $9 \times 10^4 \text{ NC}^{-1}$ at a distance of $2 \text{ cm}$. Calculate the electric field produced at a distance of $3 \text{ cm}$.

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