Question

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.

Answer 1

lectric field produced by the infinite line charges at a distance $d$ having linear harge density $\lambda$ is given by the relation,
$$\Rightarrow \lambda=2 \pi \varepsilon_{0} d E$$
$$E=\frac{\lambda}{2 \pi \varepsilon_{0} d}$$
$$\begin{aligned} &\text { Where, } \mathrm{d}=2 \mathrm{~cm}=0.02 \mathrm{~m} \\ &\mathrm{E}=9 \times 10^{4} \mathrm{~N} / \mathrm{C} \\ &\text { o Permittivity of free space and } 1 / 4 \pi \varepsilon_{0}=9 \times 10^{9} \mathrm{Nm}^{2} \mathrm{C}^{-2} \end{aligned}$$
Therefore
$$\lambda=\frac{0.02 \times 9 \times 10^{4}}{2 \times 9 \times 10^{9}}$$
$=10 \mu \mathrm{C} / \mathrm{m}$
Therefore, the linear charge density is $10 \mu \mathrm{C} / \mathrm{m}$.

Answer 2

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Answer 3

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