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**You have a summer intern position at a laboratory that uses a high-speed proton beam. The protons exit the machine at a speed of 2.10 times 10^6 m/s, and you've been asked to design a device to stop the protons safely. You know that protons will embed themselves in a metal target, but protons traveling faster than 2.20 times 10^5 m /s emit dangerous x rays when they hit. You decide to slow the protons to an acceptable speed, then let them hit a target. You take two metal plates, space them 1.70 cm apart, then drill a small hole through the center of one plate to let the proton beam enter. The opposite plate is the target in which the protons will embed themselves.**

What are the minimum surface charge densities you need to place on each plate?

HINT: ENERGY CONSIDERATION

**2. Homework Equations**

Im not even too sure how to approach the problem.... I know that a parralell plate capacitor emits the same charge on each plate... Is that what these plates will be? Im guessing it could be because the charge is apparently the same on both since the question has only one answer.

the beam goes through one of the plates and towards the other so I would assume the plate the proton goes through will be Positive charge so it will want to go towards and away from it and the Other plate a negative charge?

I am not sure but I think kinematics is involved here, I do have a distance. so x(t)=v(x)*t, solve for t and s(t)=Vt+.5*a*t, solve for a. I know E plane=(surface charge)/(2*epsilon). and I know a=(eE/m). So I can solve for the E field to find the surface charge??

Im not even too sure how to approach the problem.... I know that a parralell plate capacitor emits the same charge on each plate... Is that what these plates will be? Im guessing it could be because the charge is apparently the same on both since the question has only one answer.

the beam goes through one of the plates and towards the other so I would assume the plate the proton goes through will be Positive charge so it will want to go towards and away from it and the Other plate a negative charge?

I am not sure but I think kinematics is involved here, I do have a distance. so x(t)=v(x)*t, solve for t and s(t)=Vt+.5*a*t, solve for a. I know E plane=(surface charge)/(2*epsilon). and I know a=(eE/m). So I can solve for the E field to find the surface charge??

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