Question

$A$ straight cylindrical wire of infinite length produces electric field of $9\times {10}^4{\text{NC}}^{-1}$ at a distance of $10\text{cm}$. Linear charge density of wire is

​​​​​​​$[$1 Mark$]$

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

Answer 1

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

Electric field intensity $E=9\times {10}^4{\text{NC}}^{-1}$
distance, $r=10\text{cm}={10}^{-1}\text{m}$
We know
Electric field intensity at a distance $r$ due to an infinitely long cylindrical wire

$E=\frac{\lambda }{2\pi {ϵ}_{0}r}$

We know that $\frac{1}{4\pi {ϵ}_0}=9\times {10}^9$

$\therefore E=\frac{2\lambda }{4\pi {ϵ}_{0}r}$

$9\times {10}^4=\frac{2\lambda \times 9\times {10}^9}{{10}^{-1}}$

$\Rightarrow \lambda =0.5\times {10}^{-6}\frac{\text{C}}{\text{m}}$

$\lambda =0.5\frac{\mu \text{C}}{\text{m}}$

$\therefore$ option (b) is correct