Particle Accelerator problem with a proton beam hitting a target

[OmegaFury]

Homework Statement

In a certain particle accelerator, a current of 300μA is carried by a 4.00-MeV proton beam that has a radius of 1.30 mm. The mass of a proton is 1.67 x 10^-27kg. If the beam hits a target, how many protons hit the target in 3s?

Homework Equations

The only equation that even remotely comes to mind regarding this problem is I=e²n(tau)AE/m_e

I do not know which variable has the electron volt unit, or an equation involving current and time.

The Attempt at a Solution

I don't even know where to begin as I don't know a suitable formula to solve the problem. Perhaps if I knew that, I could get somewhere.
--Also, for personal curiosity-- In the formula for current that I listed, what exactly is tau?
Also, is n the number of particles, or the number density? And is E the electric field? My book didn't exactly break the formula down as well as I'd like.

 

[Dick]

If you don't know what the formula means then it's useless. What does an ampere (the A in your formula) mean? I think they gave you a lot of numbers in that problem that don't really matter. Try to understand what an ampere is first.

 

[OmegaFury]

Okay. Well. An ampere is equal to 1C/1s. So I guess that is where the time would come in. 300μA= 300 x 10^-6A = 300 x 10^-6C/S. So would I just multiply that by 3s to cancel the seconds, leaving only coulombs? Then divide by 1.60 x 10^-19C (I suppose that would be the charge of one proton). Which would equal 5.625 x 10¹⁵ protons.

I highly doubt this is the case because I'm sure the radius has some influence on how many protons hit the target.

 

[Dick]

Okay. Well. An ampere is equal to 1C/1s. So I guess that is where the time would come in. 300μA= 300 x 10^-6A = 300 x 10^-6C/S. So would I just multiply that by 3s to cancel the seconds, leaving only coulombs? Then divide by 1.60 x 10^-19C (I suppose that would be the charge of one proton). Which would equal 5.625 x 10¹⁵ protons.

I highly doubt this is the case because I'm sure the radius has some influence on how many protons hit the target.

But they don't give you the target size, do they? How can you use the beam radius?

 

[OmegaFury]

I'm assuming that the target is two-dimensional and is as big as the cross-sectional area of the beam.

 

[Dick]

I'm assuming that the target is two-dimensional and is as big as the cross-sectional area of the beam.

So am I. So the whole beam hits the target. So how can changing the radius change the number of particles hitting the target?

 

[OmegaFury]

Oh. I think I see what you're getting at. Electric current already incorporates the cross-sectional area as part of the equation. When calculating for the number of protons, you do calculate for the total number that hit that area over time. Looking back at it, the answer does seem to be in the ballpark. It was a multiple choice answer in which all of the answers were wrong. However, all of them are in the 10¹⁵ range, which agrees with my answer.

 

[Dick]

Oh. I think I see what you're getting at. Electric current already incorporates the cross-sectional area as part of the equation. When calculating for the number of protons, you do calculate for the total number that hit that area over time. Looking back at it, the answer does seem to be in the ballpark. It was a multiple choice answer in which all of the answers were wrong. However, all of them are in the 10¹⁵ range.

I don't see how to get an answer much different from what you got in post 3. Unless they forgot to include part of the problem or something.

 

[OmegaFury]

I'm pretty certain that was the way to go about solving it. Thanks for the help. I appreciate it.