# What Forces Affect an Electron in a Particle Accelerator?

• tarkin
In summary, the conversation discusses the calculation of electric and magnetic fields using Gauss' and Ampere's laws for an electron beam with uniform charge density and a radius R. The direction of the force on an electron in the beam is determined using the right hand rule, and it is found that the magnetic force is directed towards the center of the beam perpendicular to its current velocity. The repulsive electric force may balance this, but this can be confirmed by using the results from part (a). The conversation also briefly mentions the Large Hadron Collider and its use of magnets to direct particles, but further details are not provided.
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!

tarkin said:
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.

Last edited:

## 1. What is the force on a charge in a beam?

The force on a charge in a beam is the force exerted on a charged particle when it is placed in an electric or magnetic field created by a beam of charged particles. The magnitude and direction of the force depends on the charge of the particle, the strength of the field, and the velocity of the charged particles in the beam.

## 2. How is the force calculated?

The force on a charge in a beam is calculated using the equation F=qE+qvxB, where q is the charge of the particle, E is the electric field, v is the velocity of the particle, and B is the magnetic field. This equation takes into account both the electric and magnetic components of the force.

## 3. What is the difference between electric and magnetic fields?

An electric field is created by stationary charges, while a magnetic field is created by moving charges. In a beam, both electric and magnetic fields can be present, and the force on a charge will depend on both of these fields.

## 4. How does the velocity of the charged particles affect the force on a charge?

The velocity of the charged particles in the beam affects the force on a charge in two ways. First, a higher velocity will result in a stronger magnetic force, as the force is proportional to the velocity. Second, a higher velocity will cause the charged particle to experience a larger electric force due to the Lorentz force, which is also proportional to the velocity.

## 5. Can the force on a charge in a beam be controlled?

Yes, the force on a charge in a beam can be controlled by adjusting the strength of the electric and magnetic fields, as well as the velocity of the charged particles. This can be done using various tools such as electrodes and magnets, allowing for precise manipulation of the force on a charged particle in a beam.

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