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Guass's Law?

  • Thread starter m84uily
  • Start date
  • #1
33
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Homework Statement


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?

Homework Equations



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.
 

Answers and Replies

  • #2
ehild
Homework Helper
15,477
1,854
You know that free charges can not exist inside a metal so what do you mean on Qin?
The surface charge density is not uniform on the surface of a needle, and the tip of a needle is not flat.
You also might remember that Q/ε0 electric field lines originate from a unit positive charge, and the electric field strength is the number of field lines traversing a normal unit surface.

So the electric field strength given is related directly to the surface charge density on the metal.

ehild
 
  • #3
33
0
You definitely cleared up a lot for me! Thanks!

So:

Q/ε0 = E

Q = E(ε0)
 
  • #4
ehild
Homework Helper
15,477
1,854
It is not charge (Q) but surface charge density (σ). But the result is OK.

ehild
 

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