First of all,
The electric field at the surface of the sphere is given by
E = kQ/r²
The field strength at which breakdown occurs in the air is 3.0 MV/m
So, E = 3.0 MV/m
The sphere potential is defined as
V = kQ/r
If we divide E/V we get
E = V/r
r = V/E = 20000V / 3.10^6 V/m = 6.66 10^-3 m = 6.66 mm
2. Charge
V = kQ/r .............>>
Q = Vr/k = 20000V *( 6.66 10^-3 m)/ (9.10^9 N m2/C2) = 1.481 10^-8 C
