1) 333.6 C
In order to have breakdown, the electric field at the surface of the cloud must be equal to the breakdown electric field:
The electric field strength at the surface of a charged sphere is given by
where
is the vacuum permittivity
Q is the charge on the sphere
R is the radius of the sphere
Here we have a cloud of radius
So we can re-arrange the previous equation in order to find the charge on the cloud:
2) excess electrons
The total charge of the cloud must be (in magnitude)
Q = 333.3 C
We know that one electron carries a charge of
The total charge is just given by the charge of each electron multiplied by the number of excess electrons in the cloud:
where
N is the number of excess electrons
Solving for N, we find: