Does a stationary electron in magnetic field experience Lorentz force?

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SUMMARY

An electron that is stationary in a magnetic field does not experience a Lorentz force. The Lorentz force is defined by the equation F = Q(E + u × B), where E is the electric field, u is the velocity vector, and B is the magnetic field. In this scenario, since both the electric field E and the velocity u are zero, the resulting force F is also zero, confirming that no Lorentz force acts on the stationary electron. This conclusion is supported by the principles of Newton's laws, where the net force is zero when acceleration is zero.

PREREQUISITES
  • Understanding of Lorentz force and its equation F = Q(E + u × B)
  • Basic knowledge of Newton's laws of motion
  • Familiarity with vector operations, particularly cross products
  • Concept of electric and magnetic fields
NEXT STEPS
  • Study the implications of stationary charges in electromagnetic fields
  • Explore the relationship between electric fields and magnetic fields in electromagnetic theory
  • Learn about the behavior of charged particles in non-uniform magnetic fields
  • Investigate applications of Lorentz force in particle accelerators
USEFUL FOR

Students of physics, particularly those studying electromagnetism, educators teaching concepts of force and motion, and researchers exploring particle dynamics in magnetic fields.

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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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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.
 
Thank you HallsofIvy!
 

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