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An infinite line charge produces a field of $9 \times 10^4 \mathrm{~N} /$ $\mathrm{C}$ at a distance of $2 \mathrm{~cm}$. Calculate the linear charge density.
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Verified Answer
Given, $\mathrm{E}=9 \times 10^4 \mathrm{~N} \mathrm{C}^{-1}$
$$
\mathrm{r}=2 \mathrm{~cm}=2 \times 10^{-2} \mathrm{~m}, \lambda=\text { ? }
$$
By formula, $\mathrm{E}=\frac{\lambda}{2 \pi \varepsilon_0 \mathrm{r}}$ or $\lambda=2 \pi \varepsilon_0 \mathrm{rE}$
$$
=\frac{2 \times 10^{-2} \times 9 \times 10^4}{2 \times 9 \times 10^9}=10^{-7} \mathrm{Cm}^{-1} \text {. }
$$
$$
\mathrm{r}=2 \mathrm{~cm}=2 \times 10^{-2} \mathrm{~m}, \lambda=\text { ? }
$$
By formula, $\mathrm{E}=\frac{\lambda}{2 \pi \varepsilon_0 \mathrm{r}}$ or $\lambda=2 \pi \varepsilon_0 \mathrm{rE}$
$$
=\frac{2 \times 10^{-2} \times 9 \times 10^4}{2 \times 9 \times 10^9}=10^{-7} \mathrm{Cm}^{-1} \text {. }
$$
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