Question

An infinite line charge produces a field of $9\times {10}^{4}N/C$ at a distance of $2cm$. Calculate the linear charge density.

• A. $0.1\mu C{m}^{-1}$
• B. $0.01\mu C{m}^{-1}$
• C. $10\mu C{m}^{-1}$
• D. $1\mu C{m}^{-1}$

Answer 1

The correct option is A $0.1\mu C{m}^{-1}$

$E=9\times {10}^4$ $N/C$

$r=2$ $cm=0.02$ $m$

Linear charge density, $\lambda =?$

Electric field produced by infinite line charge:

$E=\frac{\lambda }{2\pi {ϵ}_{o}r}$

$\therefore \lambda =E2\pi {ϵ}_{o}r$

$\Rightarrow \lambda =9\times {10}^4\times 2\times 3.14\times 8.85\times {10}^{-12}\times 0.02$

$\Rightarrow \lambda =\frac{10}{100}\times {10}^{-8}\times 100$

$\Rightarrow \lambda =0.1\times {10}^{-6}$ $C{m}^{-1}$

$\lambda =0.1$ $\mu C{m}^{-1}$