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Surface charge density problem

  1. Mar 7, 2010 #1
    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...
  2. jcsd
  3. Mar 7, 2010 #2


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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
  4. Mar 7, 2010 #3
    I don't understand. E*A = 4pikQ but you don't know A or Q...
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