Question

Infinite line charge of linear density 5 nC/m lies along line x = y in the x - y plane. The electric field at (0, 0, 4) m is

• A. $\frac{22.5}{\sqrt{2}}(-\hat{i}+\hat{j})V/m$
• B. $\frac{22.5}{\sqrt{2}}(\hat{i}-\hat{j})V/m$
• C. $-22.5\hat{k}V/m$
• D. $22.5\hat{k}V/m$

Answer 1

The correct option is D $22.5\hat{k}V/m$

Line charge is in x - y plane and z-axis is one of the radial lines.
Electric field is radially away from the line charge.

$\therefore E=\frac{\lambda }{2\pi {ϵ}_{0}r}=\frac{5\times {10}^{-9}}{2\pi {ϵ}_0\times 4}=22.5\hat{k}V/m$

Where $\frac{1}{2\pi {ϵ}_0}=2\times 9\times {10}^9$