# Electron's path in uniform magnetic field? Help, please

• fatcat39
In summary, the problem involves an electron entering a uniform magnetic field in three different regions, with the fields in areas 1 and 3 going into the page and the field in area 2 going out of the page. The homework equation used is F = qvB sin theta and the attempt at a solution focuses on the circular path of the electron and whether or not it changes throughout the three regions due to the constant angle between the magnetic field and velocity.
fatcat39

## Homework Statement

There are three horizontal areas side by side - a completely uniform area. Areas 1 and 3, the magnetic fields are going into the page and area 2's field is going out of the page. An electron enters area 2 (the middle region). What is its path?

## Homework Equations

F = qvB sin theta

## The Attempt at a Solution

I know it's a circular path - what I was wondering was, since in regions 1,2, and 3 the magnetic fields are all perpendicular to the velocity vector of the electron (and therefore theta stays the same), does the circular path change in any way throughout the regions?

fatcat39 said:
I know it's a circular path - what I was wondering was, since in regions 1,2, and 3 the magnetic fields are all perpendicular to the velocity vector of the electron (and therefore theta stays the same), does the circular path change in any way throughout the regions?
Are you sure the angle between the magnetic field and velocity remains the same?

I can confirm that the path of an electron in a uniform magnetic field will indeed be circular. However, the radius of the circle may vary depending on the strength of the magnetic field and the velocity of the electron. In this case, the direction of the magnetic field in each region will determine the direction of the circular path. In region 1 and 3, the magnetic field is going into the page, so the electron will move in a clockwise circular path. In region 2, the magnetic field is going out of the page, so the electron will move in a counterclockwise circular path. The circular path will not change throughout the regions as long as the magnetic field and velocity remain constant. However, if the magnetic field or velocity changes, the radius of the circular path will also change accordingly. I hope this helps with your homework.

## 1. What is the direction of the electron's path in a uniform magnetic field?

The direction of the electron's path in a uniform magnetic field is perpendicular to both the direction of the magnetic field and the direction of the electron's velocity. This direction is known as the Lorentz force.

## 2. How does the strength of the magnetic field affect the electron's path?

The strength of the magnetic field determines the magnitude of the Lorentz force acting on the electron. A stronger magnetic field will result in a greater deflection of the electron's path.

## 3. Can the electron's path be controlled in a uniform magnetic field?

Yes, the electron's path can be controlled by adjusting the strength and direction of the magnetic field. This is the principle behind devices such as MRI machines and particle accelerators.

## 4. What is the relationship between the mass and charge of the electron and its path in a uniform magnetic field?

The mass and charge of the electron are both factors in determining the strength of the Lorentz force and therefore the curvature of the electron's path in a uniform magnetic field. A heavier electron or one with a greater charge will experience a greater force and therefore a larger deflection.

## 5. Is the electron's path in a uniform magnetic field a circular motion?

No, the electron's path in a uniform magnetic field is not a perfect circle. It follows a curved path known as a helix, with a radius of curvature that depends on the strength of the magnetic field and the velocity of the electron.

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