Surface charge density(error in my work)

In summary, the conversation is about an electron being shot away from a uniformly charged plastic sheet at a high speed. The sheet is nonconducting, flat, and very large. The figure shows the electron's vertical velocity component versus time until it returns to the launch point. The question is asking for the sheet's surface charge density, which can be calculated using the equation E*ε₀=surface charge density. After attempting a solution, it was found that the electric field from an infinite plastic sheet of finite thickness is given by E = σ/(2ε0), which is twice the value previously calculated. The correct surface charge density is 2.86E-5.
  • #1
juggalomike
51
0

Homework Statement


In Figure (a), an electron is shot directly away from a uniformly charged plastic sheet, at a speed of vs = 2.00 106 m/s. The sheet is nonconducting, flat, and very large. Figure (b) gives the electron's vertical velocity component v versus time t until the return to the launch point. (The vertical axis is marked in increments of 5.00 105 m/s.) What is the sheet's surface charge density?

http://www.glowfoto.com/static_image/14-184719L/4743/jpg/09/2010/img4/glowfoto

Homework Equations


Vf=Vi+at
a=QE/M (Q = 1.609 x 10^-19, m = 9.109 x 10^-31)
E*ε₀=surface charge density (ε₀ = 8.85 x 10^-12)

The Attempt at a Solution



a=-4*10^6/14*10^-12=2.857E17
E=(2.857E17*9.109*10^-31)/(1.609*10^-19)=1617508.66
Surface charge density=1617508.66*8.85*10^-12=1.43E-5

I have tried the answer as both positive and negative and neither are working. What am i doing wrong?
 
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  • #2
If I am not mistaken, the electric field from an infinite plastic sheet of finite thickness is given by

E = σ/(2ε0)

This is a direct consequence of Gauss's Law. Your E-field is twice that.
 
  • #3
Ah your right, thanks, correct answer was 2.86E-5
 

Related to Surface charge density(error in my work)

1. What is surface charge density and why is it important in scientific research?

Surface charge density refers to the amount of electric charge present per unit area on the surface of a material. It is an important concept in scientific research because it can affect the behavior and properties of materials, such as their ability to conduct electricity or interact with other molecules.

2. How is surface charge density measured?

Surface charge density can be measured using various techniques, such as surface potential measurements, electrophoresis, and surface plasmon resonance. These methods involve applying an electric field to the surface and measuring the resulting charge distribution.

3. What factors can affect surface charge density?

Surface charge density can be influenced by several factors, including the type and concentration of ions in the surrounding solution, the nature of the surface itself, and the temperature and pH of the environment. Other factors, such as surface roughness and the presence of adsorbed molecules, can also impact surface charge density.

4. What are some applications of surface charge density in scientific research?

Surface charge density has numerous applications in scientific research, including in the development of new materials, drug delivery systems, and biosensors. It is also important in fields such as electrochemistry, colloid science, and biophysics.

5. How can errors in surface charge density measurements be minimized?

To minimize errors in surface charge density measurements, it is important to carefully control and calibrate experimental conditions, including the temperature, pH, and concentration of ions in the surrounding solution. Using multiple measurement techniques and replicating experiments can also help to reduce potential errors.

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