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

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1. Aug 20, 2015

### UF6

1. The problem statement, all variables and given/known data

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.
2. Relevant equations
C=(ε0)A/d

Capacitor Energy=1/2C*v2

3. 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

2. Aug 20, 2015

### RUber

Where did the (9)^2 come from? I assume that is supposed to be velocity?

3. Aug 20, 2015

### UF6

4. Aug 20, 2015

### RUber

edit: I was wrong.

Last edited: Aug 20, 2015
5. Aug 20, 2015

### Staff: Mentor

You already know the voltage: 10 V.

@RUber: that calculation does not make sense at all.

6. Aug 20, 2015

### UF6

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. Aug 20, 2015

### Staff: Mentor

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.

8. Aug 20, 2015

### UF6

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.

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