Force on a charge in a beam?

[tarkin]

Homework Statement

[/B]
Consider an electron beam traveling with velocity v. The total current of the beam is I.The beam is of uniform charge density and has radius R.

(a) Find E and B at r<R and r>R using Gauss' and Ampere's laws. ( This part is fine.)

(b) Consider an electron in the beam at r=R. What is the magnitude and direction of the force it experiences?
What would the force on the electron be if it were traveling in the Large Hadron Collider?

Homework Equations

Lorentz force equation: F = q(E + v x B)

The Attempt at a Solution

From the right hand grasp rule, the electron beam should generate a magnetic field curling around. If we think of the beam as directed into the page, the B field will curl anticlockwise.

The motion of an electron in the beam should be perpendicular to the magnetic field,
so the equation just becomes F=qE +qvB, and then just sub in the answers from part a, is this correct?

What's confusing me is the direction the force will be in. Using the right hand rule, I'm finding that, for one electron, the magnetic force should be directed towards the centre of the beam, perpendicular to it's current velocity. Is this correct? does the repulsive electric force balance this so the beam still goes in a straight line?
If so, wouldn't the total force on the electron just be zero? I feel like I'm definitely missing something here...

And for the short Large Hadron Collider question, I'm unsure what to say exactly. I know it uses magnets to direct the beam in a circular path, what more should I say here?Thanks in advance for any help!

 

[TSny]

From the right hand grasp rule, the electron beam should generate a magnetic field curling around. If we think of the beam as directed into the page, the B field will curl anticlockwise.

Yes.

The motion of an electron in the beam should be perpendicular to the magnetic field,
so the equation just becomes F=qE +qvB, and then just sub in the answers from part a, is this correct?

Yes

What's confusing me is the direction the force will be in. Using the right hand rule, I'm finding that, for one electron, the magnetic force should be directed towards the centre of the beam, perpendicular to it's current velocity. Is this correct?

That's correct.

does the repulsive electric force balance this so the beam still goes in a straight line?

Use your results from part (a) to see if the forces balance.

And for the short Large Hadron Collider question, I'm unsure what to say exactly. I know it uses magnets to direct the beam in a circular path, what more should I say here?

I'm not sure about this part of the question. Seems like they should give you more information. I don't think the LHC uses electron beams. Maybe they just want you to assume that in the LHC the electrons would travel very close to the speed of light.