Answer
(a) $9.39\times 10^{-7}C/m $
(b) $0.954m $
Work Step by Step
(a) We know that
$ E=\frac{\lambda}{2\pi \epsilon_{\circ}r}$
This can be rearranged as:
$\lambda=E\times 2\pi \epsilon_{\circ}r $
We plug in the known values to obtain:
$\lambda=(35,400N/C)(2\pi\times 8.85\times 10^{-12}C^2/N.m^2\times 47.7\times 10^{-2}m)$
$\lambda=9.39\times 10^{-7}C/m $
(b) We know that
$ r=\frac{\lambda}{2\pi \epsilon_{\circ}E^{\prime}}$
We plug in the known values to obtain:
$ r=(47.7\times 10^{-2}m)(\frac{35,400N/C}{\frac{1}{2}(35,400N/C)})$
$ r=0.954m $
