Parallel-plate capacitor spark

• KillerZ
In summary: The solution involves finding the electric charge (Q) and then using the equation N = Q/e to calculate the number of electrons (N) needed to create a spark between the parallel-plate capacitor. The final answer is approximately 2.1x10^11 electrons.
KillerZ

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 = $$\epsilon$$0AE

N = Q/e

The Attempt at a Solution

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

Q = $$\epsilon$$0AE

A=$$\pi$$r^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

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.

1. What is a parallel-plate capacitor spark and how does it work?

A parallel-plate capacitor spark is a type of electrical discharge that occurs between two parallel metal plates separated by a small distance and filled with an insulating material. When a high voltage is applied to the plates, it creates an electric field between them that causes electrons to jump from one plate to the other, creating a spark.

2. What factors affect the intensity of a parallel-plate capacitor spark?

The intensity of a parallel-plate capacitor spark is affected by several factors, including the distance between the plates, the voltage applied, and the properties of the insulating material between the plates. A larger distance between the plates will result in a weaker spark, while a higher voltage and a lower dielectric constant of the insulating material will result in a stronger spark.

3. What is the significance of parallel-plate capacitor sparks in everyday life?

Parallel-plate capacitor sparks are commonly used in electronic devices, such as television and computer screens, to create images. They are also used in air purifiers to create ozone, a powerful oxidizing agent that can eliminate odors and pollutants. Additionally, parallel-plate capacitor sparks are used in spark plugs in car engines to ignite the fuel-air mixture.

4. How can parallel-plate capacitor sparks be dangerous?

Parallel-plate capacitor sparks can be dangerous if not properly controlled. They can cause fires if they occur near flammable materials, and their strong electric fields can damage electronic devices. Additionally, high voltages used to create these sparks can be harmful to humans if they come in contact with them.

5. How are parallel-plate capacitor sparks studied and measured in a laboratory setting?

In a laboratory setting, parallel-plate capacitor sparks can be studied and measured using various instruments, such as a high-voltage power supply, an oscilloscope, and a spark discharge tube. Scientists can manipulate the distance between the plates, the voltage, and the insulating material to observe the effects on the spark and collect data for further analysis and research.

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