Protons in a particle accelerator

[AliAliAli]

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?

Homework Equations

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!

 

[LowlyPion]

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?)

 

[nlightner]

Hi there! It seems like you have a good understanding of the concepts involved in this problem. Let's break down the information given and see if we can come up with a solution.

First, we know that the initial current in the accelerator is I, and the total number of particles is n. This means that the current per particle is I/n. We also know that the magnetic flux through the beam circuit changes at a rate of p Wb/s, which means that the emf (electromotive force) is p volts. We can use the equation I=q/t to find the charge per particle, q, which is equal to I/n.

Next, we can use the equation emf = dflux/dt to find the rate of change of flux, dflux/dt. We already know that the emf is p volts, so we just need to solve for dflux. This gives us dflux = p dt.

Now, we can use the equation R=(mv)/qB to find the velocity of the particles, v. We know the mass and charge of the protons, as well as the radius of the accelerator, so we just need to solve for B. This gives us B=(mv)/Rq.

Finally, we can put all of this information together to find the current after one turn of the particles. Since the radius of the beam track remains unaltered, the velocity of the particles will also remain constant. This means that the magnetic field, B, will also remain constant. Therefore, the current after one turn will be the same as the initial current, I, which is equal to I/n.

I hope this helps to clarify the problem for you. Keep up the good work!