How Many Electrons Cause a Spark in a Parallel-Plate Capacitor?

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Homework Help Overview

The discussion revolves around calculating the number of electrons transferred between the plates of a parallel-plate capacitor to create a spark, given the breakdown electric field strength of air and the dimensions of the capacitor plates.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the application of the formula for charge in a capacitor and the relationship between charge and the number of electrons. Some participants express uncertainty about the correctness of the calculations presented, while others question specific steps in the reasoning.

Discussion Status

There is an ongoing examination of the calculations provided, with some participants attempting to verify or challenge the results. A few have shared their own calculations, leading to a discussion about significant figures and the accuracy of the original solution.

Contextual Notes

Participants are working with varying numerical values and are encouraged to clarify their specific problems to facilitate better assistance. There is a noted emphasis on the importance of significant figures in the calculations.

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Homework Statement



Air "breaks down" when the electric field strength reaches 3 x 10^6 N/C, causing a spark. A parallel-plate capacitor is made from two 4.0cm-diameter disks. How many electrons must be transferred from one disk to the other to create a spark between the disks?

Homework Equations



Q = \epsilon0AE

N = Q/e

The Attempt at a Solution



Ok, I think this is right but I am not sure:

Q = \epsilon0AE

A=\pir^2

=(8.85x10^-12 C^2/Nm^2)(\pi(0.02m)^2)(3x10^6 N/C)

=3.3x10^-8 C = 33nC

N = Q/e

= (3.3x10^-8 C)/(1.60x10^-19 C/electron)

= 2.1x10^11 electrons
 
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I'm trying to figure out this same problem only with diff. numbers and I'm stuck.. so if anyone has any ideas, please share!
 
rebeccc said:
I'm trying to figure out this same problem only with diff. numbers and I'm stuck.. so if anyone has any ideas, please share!

Perhaps if you post your problem, with what you are having trouble reconciling, someone may be able to help clarify things?
 
The problem is already posted above.
 
OK.

What don't you understand about the solution he posted?
 
It's not correct, is it?
 
What step do you think is incorrect?
 
I used the same process! The only thing i did differently was use more significant figures. When done in this manner you get 2.08335*10^11 electrons.

The correct equations were used to solve this problem.
 

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