Does a stationary electron in magnetic field experience Lorentz force?

[ZedCar]

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.

 

[HallsofIvy]

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.

 

[ZedCar]

Thank you HallsofIvy!