Surface charge density problem

In summary, the minimum surface charge density for producing a spark is 3.54*10-5 C/m2, which was obtained using Coulomb's law and Gauss' law. The electric field strength must exceed 4.00×106 N/C at the tip of a metal needle for air to break down and create a spark. This can be represented by the equation E.A = 4 pi k Q, where E is the electric field strength, A is the area, and Q is the charge enclosed within that area.
  • #1
Linus Pauling
190
0
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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  • #2
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
 
  • #3
I don't understand. E*A = 4pikQ but you don't know A or Q...
 

FAQ: Surface charge density problem

1. What is surface charge density?

Surface charge density is defined as the amount of electric charge per unit area on the surface of a material. It is typically denoted by the symbol σ and is measured in units of coulombs per square meter (C/m^2).

2. How is surface charge density calculated?

Surface charge density can be calculated by dividing the total charge on the surface of a material by the surface area. This is represented by the equation σ = Q/A, where Q is the total charge and A is the surface area.

3. What factors affect surface charge density?

The main factors that affect surface charge density are the type of material, the surface area, and the amount of charge present on the surface. Other factors such as temperature, humidity, and presence of other materials can also have an impact.

4. Why is surface charge density important?

Surface charge density is important in understanding the behavior of materials in electric fields. It plays a crucial role in the study of electrostatics and can also affect the interactions between materials, such as adhesion and repulsion.

5. How is surface charge density used in practical applications?

Surface charge density is used in a variety of practical applications, including in the development of electronic devices, such as capacitors and transistors. It is also important in surface chemistry and plays a role in processes such as electroplating and corrosion prevention.

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