# Quantitative Analysis of Electron Motion in a Uniform Magnetic Field

• lloyd21
In summary: The deflection is in a direction perpendicular to both the field and the direction of motion of the electron. So if the magnetic field is vertically from top to bottom, and the path of the electron is moving east, then the only way it can be perpendicular to both is to move out of the page or into the page?
lloyd21

## Homework Statement

A beam of electrons travels east at speed, v = 6.10x 10^6 m/s . It passes through a magnetic field , B = 0.450T , directed from top to bottom. Describe exactly the path of the electrons motion?

## The Attempt at a Solution

The path of a charged particle moving in a plane perpendicular to a uniform magnetic field is a circle. The electron is moving east at v = 6.10x10^6m/s and the force on it deflects it downward. Because the force is always perpendicular to v, the magnitude of v does not change, and the electron moves at a constant speed. The electron moves clockwise in a circle.

I think this is right but I was told after to answer it , quantitatively? Eg. How large is the circle.

How can I show that? Thanks!

lloyd21 said:

## Homework Statement

A beam of electrons travels east at speed, v = 6.10x 10^6 m/s . It passes through a magnetic field , B = 0.450T , directed from top to bottom. Describe exactly the path of the electrons motion?

## The Attempt at a Solution

The path of a charged particle moving in a plane perpendicular to a uniform magnetic field is a circle. The electron is moving east at v = 6.10x10^6m/s and the force on it deflects it downward. Because the force is always perpendicular to v, the magnitude of v does not change, and the electron moves at a constant speed. The electron moves clockwise in a circle.

I think this is right but I was told after to answer it , quantitatively? Eg. How large is the circle.

How can I show that? Thanks!
Check the deflection direction that you've claimed. Won't it change continuously of the path is circular? What's the initial direction of deflection?

For the calculation you'll want to look up the force experienced by a charge moving through a magnetic field. Then think circular motion...

The force would be 4.39x10^-13 N, and I should equate that with the centripetal force right? Except that gives me r= m (6.10x10^6 m/s) / (1.60x10^-19C) ( 0.450T) ...the initial direction of deflection would be downward?

lloyd21 said:
The path of a charged particle moving in a plane perpendicular to a uniform magnetic field is a circle.
Yes, and it's a circle in that plane. So what is the geometric relationship between the magnetic field lines and the circular path?
lloyd21 said:
the force on it deflects it downward
The magnetic field is vertical, right? It's a magnetic field, not an electrostatic field.

lloyd21 said:
Except that gives me r=
Are you saying it gives the wrong answer? What answer do you get? How do you know it's wrong?

I don't think its right because of my equation from what I showed above ^

And why is deflection of is downward wrong?

lloyd21 said:
And why is deflection of is downward wrong?
The magnetic field is oriented vertically. The electron's deflection must be in a direction perpendicular to both the field and the direction of motion of the electron.

So if the magnetic field is vertically from top to bottom, and the path of the electron is moving east, then the only way it can be perpendicular to both is to move out of the page or into the page?

lloyd21 said:
So if the magnetic field is vertically from top to bottom, and the path of the electron is moving east, then the only way it can be perpendicular to both is to move out of the page or into the page?
Right. Or put another way, if the field is vertical then the deflection must be horizontal.

So using the right hand rule, it moves clockwise in a circle, which is into the page?

lloyd21 said:
So using the right hand rule, it moves clockwise in a circle, which is into the page?
If the electron had a positive charge that would be true...

The right hand rule assumes that it is a positive charge that's moving in the magnetic field. Either switch to the left hand rule for the electron or reverse the direction that the right hand rule gives you.

Ive never used the left hand rule haha! So your saying flip what I just said, so it would be deflected towards me (out of the page) and would rotate counterclockwise

lloyd21 said:
Ive never used the left hand rule haha! So your saying flip what I just said, so it would be deflected towards me (out of the page) and would rotate counterclockwise
The sense of the rotation depends upon your point of view. If viewed from "above" it will turn clockwise. If viewed from "below" it will turn counterclockwise.

But the deflection is on the horizontal plane regardless...how do I get the size of the circle, I equated the force experienced by a charge moving through a magnetic field which I got 4.39 x10^-13 N. Then think circular motion should be r = (mv/qb) , but I cannot find m? I get r = m (6.10x 10^6m/s) / (1.50x10^-19 C)( 0.450 T)

You should be able to look up the charge and mass of an electron. They are fundamental constants.

Centripetal Force = 7.8 x10^5 m
Magnetic Force = 4.39x10^-13 N

if they have to equal each other, would I use F= m (v^2) / r ?

I used r= (mv) / (qB) from before and found 7.8 x10^5 m...im not sure how to equate them when I found both answers?

Nevermind, I used Bqv = mv^2 / r

so r = (9.1 x 10^-31kg)(6.10x10^6m/s) ^2 / (4.39x10^-13N)

resulting in = 7.7 x 10^-5 m

lloyd21 said:
Centripetal Force = 7.8 x10^5 m
Magnetic Force = 4.39x10^-13 N

if they have to equal each other, would I use F= m (v^2) / r ?

I used r= (mv) / (qB) from before and found 7.8 x10^5 m...im not sure how to equate them when I found both answers?
The equation r= (mv) / (qB) is derived from F=qBv and F=mv2/r. There's nothing to be gained by going around that loop again.
You know q, B and v, and you can look up m. So calculate r.

I did that above ^^^, does that look correct? very small circle.

lloyd21 said:
I did that above ^^^, does that look correct? very small circle.
It's a very strong field.

Thanks for the help!

## 1. What is the path of an electron?

The path of an electron is the trajectory or route that an electron takes when moving through a material or medium. It is the course of its movement from one point to another.

## 2. What causes electrons to move?

Electrons are negatively charged particles that are attracted to positively charged particles. This attraction, along with the repulsion of other electrons, causes electrons to move and flow through materials.

## 3. How do electrons move in an electric field?

Electrons move in an electric field by experiencing a force that causes them to accelerate. This force is due to the difference in electric potential between two points, which creates an electric field.

## 4. Can electrons move in a vacuum?

Yes, electrons can move in a vacuum. In fact, they are able to move more easily in a vacuum because there is no resistance from other particles. This is why electrons are used in vacuum tubes and cathode ray tubes.

## 5. Do electrons always follow a straight path?

No, electrons can follow a curved or zigzag path, depending on the material they are moving through and the forces acting on them. In some cases, electrons can even move in a circular path, such as in a magnetic field.

• Introductory Physics Homework Help
Replies
31
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
491
• Introductory Physics Homework Help
Replies
6
Views
802
• Introductory Physics Homework Help
Replies
11
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
252
• Introductory Physics Homework Help
Replies
25
Views
4K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
8
Views
2K