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)

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 $
$=4 \, C / m$