Velocity of a Proton in a Capacitor

In summary, the problem involves a proton being fired from a charged capacitor and requires knowledge of conservation of energy and equations such as 1/2mv2 = (KeQq)/r and V = U/Q. The solution also involves finding the distance between the plates and the charge on the capacitor, which may need to be derived from other equations.
  • #1
joshszman09
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(1). Homework Statement

Suppose a proton is fired from the negative plate of a capacitor charged up to 1000 Volts. How fast must it be traveling to reach the other side?(2) Relevant equations

Okay, so I figured that this would be a conservation of energy problem and used: 1/2mv2 = (KeQq)/r
I think this would work, but it requires that you know both the charge on the capacitor and the distance between the plates which is not given. I am really stuck and could use some help. I just need to be pushed in the right direction and hinted towards what to do. I have literally tried everything I know about voltage and capacitors and just can't get it. If you need and more info/have questions just let me know. Thanks in advance!

3. Attempt at Solution

There isn't much to put here except a few of the equations I tried using.

I know that V = U/Q and that U= (KQq)/r and so I came up with V = (Kq)/r and tried solving for r(distance between the plates), but I got a really small number, r = 1.44E^-12. Even if that is right, I still can't think of a way to solve for the charge, Q, on the capacitor and plug the numbers into the equation I wrote in (2)
 
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  • #2
If you are given the voltage, and you know the charge on the proton, then you should have the energy that the field is supplying to the proton. This energy is converted into the kinetic energy (1/2)mv2.
 

1. What is the definition of velocity of a proton in a capacitor?

The velocity of a proton in a capacitor refers to the speed at which a proton moves within the electric field of a capacitor. This velocity is determined by the strength of the electric field and the mass of the proton.

2. How is the velocity of a proton in a capacitor calculated?

The velocity of a proton in a capacitor can be calculated using the equation v = qE/m, where v is the velocity, q is the charge of the proton, E is the strength of the electric field, and m is the mass of the proton.

3. Does the velocity of a proton in a capacitor change over time?

Yes, the velocity of a proton in a capacitor can change over time. This is because the strength of the electric field can change, which will affect the velocity of the proton.

4. How does the distance between the capacitor plates affect the velocity of a proton?

The distance between the capacitor plates does not directly affect the velocity of a proton. However, it does affect the strength of the electric field, which in turn will affect the velocity of the proton.

5. Can the velocity of a proton in a capacitor be greater than the speed of light?

No, the velocity of a proton in a capacitor cannot be greater than the speed of light. According to the theory of relativity, the speed of light is the maximum speed at which any object can travel.

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