Surface charge density problem

[Linus Pauling]

1. A spark occurs at the tip of a metal needle if the electric field strength exceeds 4.00×106 N/C, the field strength at which air breaks down. What is the minimum surface charge density for producing a spark?



2. surface charge density = Q/A



3. The answer is 3.54*10^-5 C/m². How was this obtained? I couldn't figure out by playing with dimensions...

 

[lightgrav]

Gauss' Law ...
Starting with Coulomb's kQ/r^2 = E , move the r^2 over with the E .
... x 4 pi , and it looks like the E-field is spread over a surface surrounding 4 pi kQ :
=> E.A = 4 pi k Q ... E has to pierce the Area A , which has to enclose charge Q

 

[Linus Pauling]

I don't understand. E*A = 4pikQ but you don't know A or Q...