Answer
(a) $N_e = 4.63\times 10^{21}~electrons$
(b) The electrons must move a distance of $~4.3\times 10^{-12}~m$
Work Step by Step
(a) We can find the number of conduction electrons $N_e$:
$N_e = n_e~V$
$N_e = n_e~\pi~r^2~d$
$N_e = (5.90\times 10^{28}~electrons/m^3)~(\pi)~(0.5\times 10^{-3}~m)^2~(0.10~m)$
$N_e = 4.63\times 10^{21}~electrons$
(b) We can find the required number of electrons:
$N = \frac{32\times 10^{-9}~C}{1.6\times 10^{-19}~C} = 2.0\times 10^{11}~electrons$
We can find the distance the electrons must move:
$x = \frac{2.0\times 10^{11}~electrons}{4.63\times 10^{21}~electrons}\times (0.10~m)$
$x = 4.3\times 10^{-12}~m$
The electrons must move a distance of $~4.3\times 10^{-12}~m$
