Question

A straight cylindrical wire of infinite length produces an electric field of strength $9\times {10}^4\text{N/C}$ at a distance of $10\text{cm}$ from wire. The linear charge density of the wire is:

• A. $0.1\mu \text{C/m}$
• B. $0.5\mu \text{C/m}$
• C. $50\mu \text{C/m}$
• D. $10\mu \text{C/m}$

Answer 1

The correct option is B $0.5\mu \text{C/m}$

Given:
$E=9\times {10}^4\text{N/C};r=10\text{cm}=0.1\text{m}$

Let $\lambda$ be the linear charge density of the wire.

For infinite long wire with uniform linear charge distribution:


$E=\frac{\lambda }{2\pi {ϵ}_{0}r}=\frac{2k\lambda }{r}$

$\Rightarrow 9\times {10}^4=\frac{2\times 9\times {10}^9\times \lambda }{0.1}$

$\Rightarrow \lambda =0.5\mu \text{C/m}$

Hence, option $\left(b\right)$ is correct.