# Protons in a particle accelerator

## Homework Statement

A very thin beam of protons is injected at non-relativistic
velocities in a circular particle accelerator of radius R. The
mass m and the charge e of the proton are known. The initial
current in the accelerator is I and the total number of
particles is n. The magnetic flux through the beam circuit
changes at a rate of p Wb/s, while the radius of the beam
track remains unaltered. What is the value of the current
after one turn of the particles?

I=q/t
emf = dflux/dt
R=(mv)/qB

## The Attempt at a Solution

I'm not exactly sure if I have understood the problem correctly.
But here is what I have got so far:
emf = dflux/dt = p Volts

protons passing per second = I/e

since flux = BA, and A is constant, then B is changing.

B=(mv)/Rq, so v of the particles must be changing.

We are just learning about magnetic fields in class and I don't know how to put all the information together in this problems. I hope someone can at least point me in the right direction. Thanks!

## Answers and Replies

LowlyPion
Homework Helper
I think the key here is that the radius of the beam in the accelerator doesn't change.

From the relationship that R = (m*v)/(q*B) , if B is changing at p Wb/s then I think your velocity is changing at 1/p m/s isn't it?

Since you have a fixed number of charges look at the effect on the time in making one circuit? (Charges per unit time being your current right?)