Motion of an electron in a Magentic Field

In summary, the conversation discusses plotting the motion of an electron in the x-y plane due to a magnetic field in the z plane. The initial position is at the origin and the initial velocity can be chosen at will. The program being used is Matlab and the equations used for plotting the motion resulted in a spiral rather than a circular motion. The reason for this is due to integration errors and the understanding that a magnetic field always applies a force perpendicular to the electron's motion.
  • #1
Wiseman101
9
0

Homework Statement


Plot the motion of an electron in the x-y plane due to a magnetic field in the z plane. The initial position is at the origin. The initial velocity can be chosen at will.

Homework Equations


F = q(vXB)

The Attempt at a Solution


The program I am using is Matlab. I tried plotting the motion using the following set of equations, but the motion was a spiral, not circular. Any pointers in the right direction would be much appreciated!
(Vx is the velocity in the x direction, x is the position, etc..)

w=q/m

Vx(i+1) = Vx(i) + w*(Vy(i)*B)*dt
x(i+1) = x(i) + Vx(i)*dt

Vy(i+1) = Vy(i) + w*( -Vx(i)*B)*dt
y(i+1) = y(i) + Vy(i)*dt
 
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  • #2
It's probably spiral in MATLAB because of integration errors. It seems you think that the motion has to be circular because a magnetic field always applies a force perpendicular to the electron's motion, and you'd be right.
 
  • #3
Well as long as my equations are right then that's ok:smile:
 

1. What is the motion of an electron in a magnetic field?

The motion of an electron in a magnetic field is circular. When an electron moves through a magnetic field, it experiences a force that is perpendicular to both its velocity and the direction of the magnetic field. This force causes the electron to move in a circular path around the magnetic field lines.

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

The strength of the magnetic field has a direct impact on the radius of the electron's circular motion. A stronger magnetic field will result in a smaller radius, while a weaker magnetic field will result in a larger radius. Additionally, a stronger magnetic field will cause the electron to move at a higher speed.

3. What is the significance of the electron's charge in its motion in a magnetic field?

The electron's charge plays a crucial role in its motion in a magnetic field. Since the electron has a negative charge, it experiences a force in the opposite direction to the force experienced by a positively charged particle moving in the same direction. This causes the electron to move in a circular path instead of a straight line.

4. Can the direction of the electron's motion in a magnetic field be reversed?

Yes, the direction of the electron's motion in a magnetic field can be reversed by changing the direction of the magnetic field itself. The electron will continue to move in a circular path, but in the opposite direction. This is because the force acting on the electron is always perpendicular to its velocity, regardless of the direction of the magnetic field.

5. How does the motion of an electron in a magnetic field affect its energy?

The motion of an electron in a magnetic field does not affect its energy. The electron's kinetic energy remains the same, but its direction changes as it moves in a circular path. However, the magnetic field can affect the electron's potential energy, which is determined by its position in the magnetic field. As the electron moves, its potential energy may increase or decrease depending on its position relative to the magnetic field lines.

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