What is the Speed and Number of Protons in a Van de Graaff Generator Beam?

[doggydan42]

Homework Statement

A Van de Graaff generator is one of the original particle accelerators and can be used to accelerate charged particles like protons or electrons. You may have seen it used to make human hair stand on end or produce large sparks. One application of the Van de Graaff generator is to create X-rays by bombarding a hard metal target with the beam. Consider a beam of protons at 1.00 keV and a current of 5.00 mA produced by the generator. (a) What is the speed of the protons? (b) How many protons are produced each second?

Homework Equations

$$I=\frac{dq}{dt}
\\ U + K = 0 \Rightarrow -\Delta U = \frac{1}{2} mv^2$$

The Attempt at a Solution

To find the speed of the protons, would I be able to use the second equation by using m being the mass of a single proton instead of all of the protons in the beam? Also, if U is negative then would I not be taking the square root of a negative number?

Thank you in advance

 

[kuruman]

All the protons are assumed to move at the same speed. You might as well calculate the speed of one of them. The protons lose potential energy and gain kinetic energy. Therefore -ΔU is a positive number.

 

[doggydan42]

So my one confusion with only using the mass of a single proton in the equation is that then wouldn't the energy be different, since it is the energy of the beam? If not, why?

Thank you.

 

[kuruman]

"Energy of the beam" means the energy of a single proton in the beam. This allows one to compare beams and what they can do when they collide with their targets. The "current" in the beam is related to the number of protons which are being produced continuously. If you know the current, you calculate the total energy that crosses a certain point per unit time. That's part (b) of the problem.