$22\mathrm{.}48($a$)$ How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere $30\mathrm{.}0$ cm in diameter to produce an electric field of magnitude

$1390$

$$

N

$/$

C

just outside the surface of the sphere? $($b$)$ What is the electric field at a point $10\mathrm{.}0$ cm outside the surface of the sphere?