Does a stationary electron in magnetic field experience Lorentz force?

In summary, when an electron is stationary in a magnetic field, it will not experience a Lorentz force because the net force is equal to zero due to the absence of an electrical field and a velocity vector.
  • #1
ZedCar
354
1

Homework Statement



If an electron is stationary in a magnetic field, will it experience a Lorentz force?


Homework Equations



The Attempt at a Solution



The total vector force (Lorentz force - F) is
F = Fe + Fm = Q(E + u X B)


The Lorentz force can also be written in terms of Newton’s law such that
F = ma = m (du/dt) = Q(E + u X B)

∴ Since the electron is stationary, acceleration equals zero and the so the electron does not experience a Lorentz Force.
 
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  • #2
Well, I not sure I like "acceleration equal zero and so the electron does not experience a Lorentz Force". If an electron is constrained to be stationary, then both velocity and acceleration are 0 so the net force is 0. Just saying that something is stationary is not enough to show that a particular force, rather than the net force, is 0.

However, in this problem, since there is no electrical field, E, and the velocity vector, u, is 0, it follows that F= Q(0+0x B)= 0 and, for that reason, there is no Lortentz force.
 
  • #3
Thank you HallsofIvy!
 

1. What is the Lorentz force?

The Lorentz force is the force experienced by a charged particle moving in a magnetic field. It is perpendicular to both the direction of motion of the particle and the direction of the magnetic field.

2. How does the Lorentz force affect a stationary electron in a magnetic field?

A stationary electron in a magnetic field will experience a Lorentz force, causing it to move in a circular path around the axis of the magnetic field. The force is equal to the charge of the electron multiplied by its velocity and the strength of the magnetic field.

3. Why does a stationary electron experience a Lorentz force in a magnetic field?

According to the Lorentz force law, any charged particle in a magnetic field will experience a force due to the interaction between its charge and the magnetic field. Since an electron has a charge, it will experience a Lorentz force in a magnetic field.

4. Can a stationary electron in a magnetic field experience a Lorentz force in the absence of an electric field?

Yes, a stationary electron in a magnetic field can experience a Lorentz force even if there is no electric field present. This is because the Lorentz force is solely dependent on the particle's charge and the magnetic field, not on the presence of an electric field.

5. How is the direction of the Lorentz force determined for a stationary electron in a magnetic field?

The direction of the Lorentz force on a stationary electron in a magnetic field is determined by the right-hand rule. If you point your thumb in the direction of the electron's velocity, and your fingers in the direction of the magnetic field, the force will be perpendicular to both, in the direction of your palm.

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