Find out the surface charge density at the intersection
Question:

Find out the surface charge density at the intersection of point $\mathrm{x}=3 \mathrm{~m}$ plane and $\mathrm{x}$-axis, in the region of uniform line charge of $8 \mathrm{n} \mathrm{C} / \mathrm{m}$ lying along the $\mathrm{z}$-axis in free space.

1. (1) $0.424 \mathrm{nCm}^{-2}$

2. (2) $47.88 \mathrm{C} / \mathrm{m}$

3. (3) $0.07 \mathrm{nCm}^{-2}$

4. (4) $4.0 \mathrm{nCm}^{-2}$

Correct Option: 1

Solution:

(1)

$\frac{2 \mathrm{~K} \lambda}{\mathrm{r}}=\frac{\sigma}{\varepsilon_{0}} \quad(\mathrm{x}=3 \mathrm{~m})$

$\sigma=0.424 \times 10^{-9} \frac{\mathrm{C}}{\mathrm{m}^{2}}$