Problem 20.57

20.57. b)
We know that
$V = E \cdot r$
so, we can find the radius by solving for it in terms of the electric field and potential.
$r = \frac{V}{E}$
We see from table 20.1 that the maximum electric field that can exist in dry air before electric breakdown is $3 \times 10^{6} V/m$.
$r = \frac{600 kV}{3 \times 10^{6} V/m}$
r = .200 m

a) Electic potential is given by
$V = \frac{k q}{r}$
Solving for q, we find
$q = \frac{V r}{k}$
$q = \frac{(600 kV)(.200 m)}{9 \times 10^{9} N m^{2}/C^{2}}$
$q = 13.3 \mu C$