# Electron helix in a magnetic field

• Basil Fawlty
In summary, the conversation discusses the possibility of focusing electrons in a parallel entry path, but it is concluded that this is not possible due to the infinite helix trajectory of the electrons. The equations for the helix are provided, but it is noted that there is no limiting case when the initial velocity tends to zero, so there is no focus. It is also suggested that the question may have been referring to a perpendicular entry path instead. The concept of focusing in a uniform magnetic field is then explored, and it is determined that the distance between two electrons with different velocities can be calculated using a simple equation. However, it is noted that this does not align with the idea of a traditional focus. Overall, it is concluded that the question is
Basil Fawlty

I thought that a nearly parallel entry path would result in a helix of very small, but constant, radius. I would not expect the electrons to focus at a point, but continue along the infinite helix. What have I missed?

I moved this thread from a technical forum. No template.

@Basil Fawlty , You must show us your attempt at the solution before our homework helpers are allowed to help. So, please show us your work, or I'll have to tell Sybil :-)

Well, producing the equations for the helix will not solve this, as the electrons will continue along the helix but not come to a focus.

Assuming magnetic field in the x direction, and v a (very small) initial velocity in the y direction (without loss of generality):

x=ut, y=(mv/eB)sin(eBt/m), z=(mv/eB)(1-cos(eBt/m))

But, of course, there is no limiting case when v tends to zero, so no focus.

I thought the question may be wrong, and 'parallel' should read 'perpendicular', so interchange u and small v in the above equations, but even then the answer provided in the question, which is the circumference of my helix, does not appear obvious.

This question is bugging me, as electrons can be focused on a screen in various devices but only by changing current in coils and so the magnetic field. Is there some physical phenomenon that can make this happen in a uniform field?

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What is the distance between two such electrons with different v?

With two different velocities v1 and v2 d(t)= (2m(v1-v2)/eB)sin(eBt/2m) is the simplest form of the distance function. Ah yes, so d(t)=0 when eBt/2m=π, t=2mπ/eB and x= 2πmu/eB
It's not intuitive at all that no matter what the initial relative y velocity component, the two electrons will always focus at a particular point in time and space based on e,m,B,u alone. Plus the question did not help by saying 'negligible interaction'!
Many thanks Dale.

Dale
I agree with you. It is a confusingly worded question. I am not sure I would call that a focus at all since to me “focus” invokes ray optics and not helical paths converging.

## 1. What is an electron helix in a magnetic field?

An electron helix is a spiral-shaped path that an electron follows when it moves through a magnetic field. This phenomenon is caused by the interaction between the magnetic field and the charged particle.

## 2. How does a magnetic field affect the path of an electron?

A magnetic field exerts a force on an electron due to its charge. This force causes the electron to move in a curved path, resulting in the spiral shape of the electron helix.

## 3. What is the significance of the electron helix in scientific research?

The electron helix is important in understanding the behavior of charged particles in magnetic fields, which has applications in fields such as particle accelerators, nuclear physics, and astrophysics. It is also a fundamental concept in quantum mechanics.

## 4. Can the direction of the electron helix be changed?

Yes, the direction of the electron helix can be changed by altering the strength or direction of the magnetic field. This is known as the Lorentz force and is described by the right-hand rule in physics.

## 5. Are there any real-world examples of electron helixes?

Yes, there are many real-world examples of electron helixes, including in the design of electron microscopes, particle accelerators, and MRI machines. The phenomenon is also observed in the auroras in Earth's atmosphere, where charged particles from the sun spiral along Earth's magnetic field lines.

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