An infinite line charge produces a field of $9 \times 10^4 \mathrm{NC}^{-1}$ at a distance of $2…

An infinite line charge produces a field of $9 \times 10^4 \mathrm{NC}^{-1}$ at a distance of $2 \mathrm{~cm}$. The linear charge density is
  1. $10^{-7} \mathrm{C} \mathrm{m}^{-1}$
  2. $1.5 \times 10^{-7} \mathrm{C} \mathrm{m}^{-1}$
  3. $10^{-8} \mathrm{C} \mathrm{m}^{-1}$
  4. $1.5 \times 10^{-8} \mathrm{C} \mathrm{m}^{-1}$

Solution

Electric field, $\mathrm{E}=9 \times 10^4 \mathrm{~N} / \mathrm{C}$ Distance, $\mathrm{r}=2 \mathrm{~cm}=0.02 \mathrm{~m}$ For infinite line change $\begin{aligned} & E=\frac{\lambda}{2 \pi \epsilon_0 r}=\frac{2 \lambda}{r} \times 9 \times 10^9 \\ & \text { Liner charges density, } \lambda=\frac{E r}{2 \times 9 \times 10^9} \\ & =\frac{9 \times 10^4 \times 0.02}{2 \times 9 \times 10^9}=10^{-7} \mathrm{Cm}^{-1}\end{aligned}$

Asked in: AP EAMCET 2023 (16 May Shift 2)

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