Could Someone Look Over My Work? (particle accelerator design problem)

In summary: Thank you for pointing me in the right direction.In summary, the conversation discusses the design of a simple particle accelerator using two oppositely charged plates with small holes. The goal is for the electron beam to gain 10.0 eV of energy, which requires a voltage difference of 1.0E+01 V between the plates. The speed of the electrons after passing through the accelerator is calculated to be 1.9E+06 m/s. The electric field strength between the plates is determined to be 3.3E+06 V/m, and the amount of electrical energy stored by the field is found to be 1.075275E-9 J.
  • #1
UF6
5
0

Homework Statement



  1. You want to construct a simple particle accelerator and hit on the following design: you will take two oppositely charged plates with small holes drilled into them and set them up parallel to each other. You will create a vacuum between the two plates and fire a beam of electrons through the small hole in the negatively charged plate, aimed so that the beam will emerge through the hole in the positively charged plate. You want the electrons in the beam to gain 10.0 eV of energy, so you need to work out what magnitude of voltage difference to set up between the two plates.
    Correct, computer gets: 1.0E+01 V

    Your electron beam consists of electrons that are initially moving at around 2.7×105 m/s. You want to work out how fast the electrons are moving after passing through your accelerator.

    Correct, computer gets: 1.9e+06 m/s

    You decide to investigate the physical details of your electron accelerator a bit more closely. You start by determining the strength of the electric field between the plates. You've set the plates up so that their separation is 3 μm.

    Correct, computer gets: 3.3E+06 V/m

    The plates you chose had areas of 9 mm^2. You want to know how much electrical energy is stored by the electric field between the plates.

Homework Equations


C=(ε0)A/d

Capacitor Energy=1/2C*v2

The Attempt at a Solution


This is fairly easy problem, which is a great reason why it's also the one that's holding me back from the entire homework set. I think I made a conversion error I just don't know where.

-(8.854E-12)(9E-6/3E-6)
=2.655E-11 C

1/2(2.655E-11)(9)2
=1.075275E-9 J
 
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  • #2
UF6 said:
This is fairly easy problem, which is a great reason why it's also the one that's holding me back from the entire homework set. I think I made a conversion error I just don't know where.

-(8.854E-12)(9E-6/3E-6)
=2.655E-11 C

1/2(2.655E-11)(9)2
=1.075275E-9 J

Where did the (9)^2 come from? I assume that is supposed to be velocity?
 
  • #4
edit: I was wrong.
 
Last edited:
  • #5
You already know the voltage: 10 V.

@RUber: that calculation does not make sense at all.
 
  • #6
mfb said:
You already know the voltage: 10 V.

@RUber: that calculation does not make sense at all.
Would you convert 10 eV into 1E19 V or leave it as so?

The answer given for either case as the final answer is 1.3275E27 J or 1.3275E-9 J. I just find the first to be rather larger.
 
  • #7
There is nothing to convert.
UF6 said:
so you need to work out what magnitude of voltage difference to set up between the two plates.
Correct, computer gets: 1.0E+01 V
"Converting 10 eV into 1E19 V" does not make sense. It's like trying to convert 1 meter to 5 kilogram of apples.
 
  • #8
mfb said:
There is nothing to convert.
"Converting 10 eV into 1E19 V" does not make sense. It's like trying to convert 1 meter to 5 kilogram of apples.
Thanks by the way. I understand how that works now a bit better after reading about electron volts to volts after I read your response.
 

Related to Could Someone Look Over My Work? (particle accelerator design problem)

1. Can you check if my design for the particle accelerator is feasible?

As a scientist, I can review your design and provide feedback on its feasibility. However, the final determination of feasibility would require testing and experimentation.

2. Is my design efficient enough for the intended purpose?

I can analyze your design and provide suggestions for increasing efficiency, but the ultimate efficiency of the particle accelerator would depend on various factors such as materials used, power source, and operational conditions.

3. Are there any major flaws or errors in my design?

I can carefully examine your design and identify any major flaws or errors that may hinder its functionality. However, it's essential to note that the design process involves trial and error, and it may require multiple iterations to achieve the desired outcome.

4. Can you suggest any improvements or modifications to my design?

Based on my knowledge and experience, I can provide recommendations for improving your design. However, it is crucial to consider all aspects of the design, including safety, cost, and feasibility, before making any modifications.

5. How long will it take for you to review my design?

The time required to review your design would depend on the complexity and size of the particle accelerator, as well as my current workload. I will strive to provide feedback in a timely manner, but it may take several days to thoroughly examine and analyze your design.

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