Question

The electric field at a point $2$cm from an infinite line charge of linear charge density ${10}^{-7}$ $C{m}^{-1}$ is?

• A. $4.5\times {10}^{4}N{C}^{-1}$
• B. $9\times {10}^{4}N{C}^{-1}$
• C. $9\times {10}^{2}N{C}^{-1}$
• D. $18\times {10}^{4}N{C}^{-1}$

Answer 1

The correct option is B $9\times {10}^{4}N{C}^{-1}$

$\text{Step 1: Electric field due to infinitely long charged wire}$

Linear charge density of wire, $\lambda ={10}^{-7}C{m}^{-1}$

Electric field at a distance $r$ from infinitely long charged wire is given by,

$E=\frac{\lambda }{2\pi {ϵ}_{o}r}$ $......\left(1\right)$

$\text{Step 2: Substituting the values in equation (1)}$

$E=\frac{{10}^{-7}}{2\pi \times 8.85\times {10}^{-12}\times 0.02}=9\times {10}^{4}N{C}^{-1}$

Hence, Option (B) is correct.