Question

An infinitely long wire is kept along $z$ -axis from $z=- \, \in fty \, $ to $ \, z= \, + \, \infty$ , having uniform linear charge density $\frac{10}{9} \, nC \, m^{- 1}$ The electric field $\overset{ \rightarrow }{E}$ at point $\left(6 \, cm , \, 8 \, cm , \, 10 \, cm\right)$ will be:

• A. $\left(\right. 160 \, \hat{i} + 120 \, \hat{j} + 200 \, \hat{k} \left.\right) \, N \, C^{- 1}$
• B. $\left(\right. 200 \, \hat{k} \left.\right) \, N \, C^{- 1}$
• C. $\left(\right. 160 \hat{i} + 120 \hat{j} \left.\right)NC^{- 1}$
• D. $\left(\right. 120 \hat{i} + 160 \hat{j} \left.\right)NC^{- 1}$

Answer 1

Answer: (D)

$E=\frac{2 k \lambda}{d}=\frac{2 \times 9 \times 10^9 \times\left(\frac{10}{9}\right) \times 10^{-9}}{10 \times 10^{-2}}=200 \quad \mathrm{~V} \mathrm{~m} \mathrm{~m}^{-1}$
As field is radial out, there is no component of it in $Z$ direction.
$\overset{ \rightarrow }{E}=200 \, cos53\hat{i}+200sin53\hat{j}$
$=\left(\right. 120 \hat{i} + 160 \hat{j} \left.\right)NC^{- 1}$