Question

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

• A. $47.88\text{C/m}$
• B. $0.07{\text{nC m}}^{-2}$
• C. $0.424{\text{nC m}}^{-2}$
• D. $4.0{\text{nC m}}^{-2}$

Answer 1

The correct option is C $0.424{\text{nC m}}^{-2}$

Electric field due to wire is given by, $E=\frac{2k\lambda }{r}$
Electric field due to two dimensional lamina having surface charge density $\sigma$ is given by,
$E^{\prime }=\frac{\sigma }{{\epsilon }_o}$
Equating both at the point of intersection, we get
$\frac{2k\lambda }{r}=\frac{\sigma }{{\epsilon }_0}$
$\Rightarrow 2\times \frac{1}{4\pi {\epsilon }_0}\times \frac{\lambda }{r}=\frac{\sigma }{{\epsilon }_0}$
$\Rightarrow \frac{8\times {10}^{-9}}{2\times 3.14\times 3}=\sigma$
$\Rightarrow \sigma =0.424{\text{nC m}}^{-2}$