Modeling an electron in a Magnetic Field

[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.

 

[marlon]

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

 

[Noone1982]

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.

 

[marlon]

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