# Modeling an electron in a Magnetic Field

• Noone1982
In summary, the electron experiences a force of F = qVxB in a magnetic field, which is equivalent to centripetral force. To model an electron in a magnetic field, I need to model every part of its trajectory. This is proving tricky, so I am considering an iteration approach. The mass value I used was 1.6022e-19 C and the charge to mass ratio was 1.76e11.
Noone1982
I'm not sure where to place this, so please forgive me.

As you know, an electron experiences a force of F = qVxB in a magnetic field and equating this to centripetral force, we can find the radius of the electron's path to be R = mv/qB Ok, that's simple enough.

Now, I want to model an electron via 3D graphing in a magnetic field. For this, I need to model every part of its trajectory. This is proving tricky.

Say we have:

Bx = 0
By = 0
Bz = 1 micro tesla

The initial electron is coming in at

Vx = 0
Vy = 1.5e8 m/s
Vz = 0

The cross product is

Fx = q(VyBz - ByVz)
Fy = q(VxBz - VzBx)
Fz = q(VxBy - VyBx)

Now the acceleration is just a = F / m

However, For ax I'm getting 4.23e13 m/s^2! which is a wee bit high. Ok, just plain wrong. How would you generate an animation of an electon in a magnetic field? I would like to extend it so the magnetic field osccilates and varies with amplitude versus time.

Noone1982 said:
I'm not sure where to place this, so please forgive me.

As you know, an electron experiences a force of F = qVxB in a magnetic field and equating this to centripetral force, we can find the radius of the electron's path to be R = mv/qB Ok, that's simple enough.

Now, I want to model an electron via 3D graphing in a magnetic field. For this, I need to model every part of its trajectory. This is proving tricky.

Say we have:

Bx = 0
By = 0
Bz = 1 micro tesla

The initial electron is coming in at

Vx = 0
Vy = 1.5e8 m/s
Vz = 0

The cross product is

Fx = q(VyBz - ByVz)
Fy = q(VxBz - VzBx)
Fz = q(VxBy - VyBx)

Now the acceleration is just a = F / m

However, For ax I'm getting 4.23e13 m/s^2! which is a wee bit high. Ok, just plain wrong. How would you generate an animation of an electon in a magnetic field? I would like to extend it so the magnetic field osccilates and varies with amplitude versus time.

What is the mass value you used ? Besides, how do you know the value you got is too high ? What exactly did you do.

Anyhow, the approach and formula's are OK.

If you want to incorporate a t-dependent B field, you just need to integrate over time (once and twice) to get velocity and then the trajectory. How does the B field vary (sine, cosine) and along which direction (x,y,z) ? if you know this, just add the components into the right hand side of Fx, Fy and Fz. divide by m to get a and then you start the integrations...

marlon

I used the charge of an electron as 1.6022e-19 C and the mass as 9.1e-31 kg which is a charge to mass ratio of 1.76e11!

My plan was to do it iteratively. To calculate vx, vy, and vz and use rx = rx + vx*dt etc to plot the positions.

Noone1982 said:
and use rx = rx + vx*dt etc to plot the positions.
You are forgetting the $$t^2$$ term. There is a force acting on your system so you also need the $$a_x$$ part in your equation for $$r_x$$ !

marlon

## 1. How does a magnetic field affect the movement of an electron?

When an electron is placed in a magnetic field, it experiences a force perpendicular to both the direction of its velocity and the direction of the magnetic field. This force causes the electron to move in a circular or helical path, depending on the strength of the magnetic field and the speed of the electron.

## 2. What is the mathematical model used to describe the motion of an electron in a magnetic field?

The mathematical model used to describe the motion of an electron in a magnetic field is the Lorentz force law. This law states that the force on a charged particle in a magnetic field is equal to the product of the charge of the particle, the velocity of the particle, and the strength of the magnetic field.

## 3. What is the role of the magnetic field strength in modeling an electron?

The strength of the magnetic field affects the radius of the electron's circular or helical path. The stronger the magnetic field, the smaller the radius of the path will be. This means that the electron will move in a tighter circle or spiral faster in a stronger magnetic field.

## 4. How does the speed of the electron impact its movement in a magnetic field?

The speed of the electron also affects the radius of its circular or helical path. The faster the electron is moving, the larger the radius of its path will be. This means that a faster moving electron will move in a wider circle or spiral slower in a magnetic field compared to a slower moving electron.

## 5. Can the motion of an electron in a magnetic field be used in practical applications?

Yes, the motion of an electron in a magnetic field has many practical applications, such as in particle accelerators, MRI machines, and Cathode Ray Tubes (CRTs) used in televisions and computer monitors. By manipulating the magnetic field strength and the speed of the electron, scientists can control the path and velocity of the electron, allowing for precise measurements and applications in various technologies.

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