A spark occurs at the tip of a metal needle if the electric field strength exceeds 3.0x10^6 N/C.
What is the minimum surface charge density for producing a spark?
int(EdA) = (Qin) / e0
The Attempt at a Solution
I imagine the surface as a cylinder with the electric field going parallel to it.
int(EA) = backface + side + frontface = EA + EA = 2EA
E = 3.0x10^6 N/C
A = (pi)r^2
(2)(3.0x10^6 N/C)(pi)r^2 = (Qin) / e0
(e0)(2)(3.0x10^6 N/C)(pi)r^2 = Qin
Then, I don't want r is! I've probably gone about solving this all wrong, thanks in advance for your help.