An infinite line charge produces a field of
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.

Solution:

Electric field produced by the infinite line charges at a distance d having linear charge density λ is given by the relation,

$E=\frac{\lambda}{2 \pi \in_{0} d}$

$\lambda=2 \pi \in_{0} d E$

Where,

d = 2 cm = 0.02 m

$E=9 \times 10^{4} \mathrm{~N} / \mathrm{C}$

$\epsilon_{0}=$ Permittivity of free space

$\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \mathrm{~N} \mathrm{~m}^{2} \mathrm{C}^{-2}$

$\lambda=\frac{0.02 \times 9 \times 10^{4}}{2 \times 9 \times 10^{9}}$

$=10 \mu \mathrm{C} / \mathrm{m}$

Therefore, the linear charge density is $10 \mu \mathrm{C} / \mathrm{m}$.

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