Question

An infinite line charge produces a field of $18\times 10^{5}\,N/C$ at a distance of $4\,cm$ . What is the linear charge density?

• A. $18\,\mu \,C/m$
• B. $5\,\mu \,C/m$
• C. $4\,\mu \,C/m$
• D. $10\,\mu \,C/m$

Answer 1

Answer: (C)

$4\,\mu \,C/m$

Answer 2

For a infinite line charge, $E=\frac{2 \lambda}{4 \pi \varepsilon_{0} r}$
$\lambda=E\left(2 \pi \varepsilon_{0} r\right)$
$=\frac{18 \times 10^{5} \times\left(4 \times 10^{-2}\right)}{2 \times 9 \times 10^ 9}$
$=4 \times 10^{-6} C / m$
$=4 \, C / m$