Understanding Magnetism: Relating Magnetic Forces to Charged Particle Beams"

[deanchhsw]

My teacher recently gave me a task of relating magnetic forces to a beam of chraged particles moving in a straight line. To aid us in this, she also set up a guideline question, displayed below:

The diagram below shows a beam of charged particles moving in a straight line with speed v. Each particle has a charge +q and there are N particles in length L of the beam.

(diagram omitted, since the explanation above seems sufficient, direction does not seem to matter here)

a) how far do the particles travel in time "delta t"?
this seemed obvious, s = vt, hence s = v"delta t".

b) how many particles pass a given point in a time "delta t"?
how do you know that? since there is no specific point where a particle begins to travel, how would you know how many passes a random point in a specified time? I thought a lot about this, but can't seem to understand..

c) Using your answers to (a) and (b) above show that the current I carried by the beam is given by the expression I = Nvq/L.

It seems as though the first two equations relate to each other to create the final expression. But I'm lost. I know for memory that I = "delta q"/"delta t", but without knowing what to do for #b) I can't figure anything out.

If anyone could help me, (or at least guide me in the right direction?), I'll be grateful.

 

[learningphysics]

c) Using your answers to (a) and (b) above show that the current I carried by the beam is given by the expression I = Nvq/L.

It seems as though the first two equations relate to each other to create the final expression. But I'm lost. I know for memory that I = "delta q"/"delta t", but without knowing what to do for #b) I can't figure anything out.

If anyone could help me, (or at least guide me in the right direction?), I'll be grateful.

{----------------------}--------------------------------
A...v(delta t)....B

Suppose my '-' s are the beam... suppose the distance between A and B is v (delta t).

It takes the particle at A delta t seconds to reach B... in that time all the particles within the { } cross B (this is the critical part! in the time that it takes the particle at A to reach B... all the particles that were between A and B at the start cross B)... so all the particles within a length of v(delta t) cross B in delta t seconds.

You know the number of electrons in a length L... so you can get the number of electrons in a length v delta t.

 

[deanchhsw]

I see. So since N/L should be equal to n/v(delta t), with n being the answer to #b, doing the math n comes out to be N(v delta t)/L. I understand that now.

But how, then, do you incorporate that to find the current I?
OHH I solved my own question lol

I = delta q/delta t, and delta q is equal to nq, since it is the number of the particles carrying the given charge +q. So substituting nq = delta q,

I = N(v delta t)q/L(delta t), and simplifying, I = Nvq/L.

Thanks, you've been a ton of help! :)