Surface charge density problem

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To determine the minimum surface charge density required to produce a spark at a metal needle, the electric field strength must exceed 4.00×10^6 N/C, which is the breakdown threshold for air. The surface charge density is calculated using the formula Q/A, where Q is the charge and A is the area. The derived answer is 3.54×10^-5 C/m², but the calculation process is unclear to some participants. The discussion involves applying Gauss' Law and manipulating the equation E = kQ/r² to relate the electric field to the enclosed charge and area. Clarification is sought on how to derive the surface charge density without knowing the specific values of Q or A.
Linus Pauling
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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...
 
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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
 
I don't understand. E*A = 4pikQ but you don't know A or Q...
 

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