Question

An infinitely long wire is kept along $z$ -axis from $z=-\infty$ to $z=+\infty$, having uniform linear charge density $\frac{10}{9}nC/m$. The electric field at point $(6cm,8cm,10cm)$ will be

• A. $(120\hat{i}+160\hat{j}+200\hat{k})V/m$
• B. $200\hat{k}V/m$
• C. $(160\hat{i}+120\hat{j})V/m$
• D. $(120\hat{i}+160\hat{j})V/m$

Answer 1

Answer: (D)

$E=\frac{\lambda }{2\pi {\epsilon }_{0}d}=\frac{2K\lambda }{d}$
$=\frac{2\times 9\times 10^9\times (10/9)\times 10^{-9}}{10\times 10^{-2}}=200V/m$
As field is radial out, there is no component of it in $z$ -direction.

$\vec{E}=\left(200\cos 53^{\circ }\hat{i}+200\sin 53^{\circ }\hat{j}\right)V/m$
$=\left(200\times \frac{3}{5}\hat{i}+200\times \frac{4}{5}\hat{j}\right)=(120\hat{i}+160\hat{j})V/m$