Question

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

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

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