Find out the surface charge density at the intersection of point x=3 m plane and $x$-axis,

Question:

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

  1. $0.424 \mathrm{nC} \mathrm{m}^{-2}$

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

  3. $0.07 \mathrm{nC} \mathrm{m}^{-2}$

  4. $4.0 \mathrm{nC} \mathrm{m}^{-2}$


Correct Option: 1

Solution:

$\frac{2 \mathrm{~K} \lambda}{\mathrm{r}}=\frac{\sigma}{\varepsilon_{0}}$

$(x=3 m)$

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

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