Two parallel infinite line charges with linear charge densities +… - Vidyadip

MCQ

Two parallel infinite line charges with linear charge densities $+\lambda\; \mathrm{C} / \mathrm{m}$ and $-\lambda\; \mathrm{C} / \mathrm{m}$ are placed at a distance of $2 \mathrm{R}$ in free space. What is the electric field mid-way between the two line charges?

A
$0\;N/C$
B
$\frac{2 \lambda}{\pi \epsilon_{0} \mathrm{R}} \mathrm{N} / \mathrm{C}$
✓
$\frac{\lambda}{\pi \mathrm{e}_{0} \mathrm{R}} \mathrm{N} / \mathrm{C}$
D
$\frac{\lambda}{2 \pi \epsilon_{0} R} \mathrm{N} / \mathrm{C}$

✓

Answer

Correct option: C.

$\frac{\lambda}{\pi \mathrm{e}_{0} \mathrm{R}} \mathrm{N} / \mathrm{C}$

c
$\overrightarrow{\mathrm{E}}=\overrightarrow{\mathrm{E}}_{1}+\overrightarrow{\mathrm{E}}_{2}$

$\mathrm{E}=\mathrm{E}_{1}+\mathrm{E}_{2}$

$E=\frac{\lambda}{2 \pi \epsilon_{0} R}+\frac{\lambda}{2 \pi \epsilon_{0} R}$

$\mathrm{E}=\frac{\lambda}{\pi \epsilon_{0} \mathrm{R}} \mathrm{N} / \mathrm{C}$

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