What are the magnetic effects on electrons described by equations?

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A magnetic field exerts a force on moving electrons, described by the Lorentz force equation, F = q(v × B), where F is the force, q is the charge of the electron, v is its velocity, and B is the magnetic field. This force causes electrons to move in circular or helical paths, depending on their initial velocity relative to the magnetic field. The right-hand rule can be used to determine the direction of the force acting on the electron. Additionally, the magnetic field can influence the energy levels of electrons in atoms, leading to phenomena such as Zeeman splitting. Understanding these effects is crucial for applications in electromagnetism and quantum mechanics.
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what is the effect of a magnetic field on a electron?
please with equations
 
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