Magnetic force and frames of referenceI'm having a hard time trying to understand the next situation:Suppose that I have a magnet that creates a quite uniform magnetic filed B → . In the vicinity of this magnet there is a particle with charge q that is moving with velocity v → in some direction.This is, in the frame of reference of the magnet, the particle is moving with velocity v → and therefore the particle experiences a force given by: F → = q ( v → × B → ). This would cause the path of the particle to curve around the magnetic field.On the other hand, an observer situated in the particle would see the magnet moving with velocity v → ′ = − v → . How would this observer account for the movement of the magnet caused by the force F ′ ?I believe that the force F → ′ is given by the relativistic transformation: F → ′ = − γ F → Knowing that the force is perpendicular to the velocity (this is if, for instance, the particle is moving along the x axis, then the force is along the y axis).I am in the early stages of understanding relativistic mechanics so please forgive me is the question looks silly. Thanks in advance.

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Magnetic force and frames of referenceI&#039;m having a hard time trying to understand the next situation:Suppose that I have a magnet that creates a quite uniform magnetic filed             B      →      . In the vicinity of this magnet there is a particle with charge   q that is moving with velocity             v      →       in some direction.This is, in the frame of reference of the magnet, the particle is moving with velocity             v      →       and therefore the particle experiences a force given by:             F      →        =  q    (            v      →        ×            B      →        ). This would cause the path of the particle to curve around the magnetic field.On the other hand, an observer situated in the particle would see the magnet moving with velocity                     v        →              ′    =  −            v      →      . How would this observer account for the movement of the magnet caused by the force       F    ′  ?I believe that the force                     F        →              ′   is given by the relativistic transformation:                    F        →              ′    =  −  γ            F      →      Knowing that the force is perpendicular to the velocity (this is if, for instance, the particle is moving along the x axis, then the force is along the y axis).I am in the early stages of understanding relativistic mechanics so please forgive me is the question looks silly. Thanks in advance.

Ryan Underwood · Accepted Answer

There&#039;s an electric component to the Lorentz force:            F      →        =  q  (            E      →        +            v      →        ×            B      →        )In the frame of the particle where its velocity is zero, the force acting on the stationary particle would be interpreted as being electric, since the magnetic field                     B        ′            →       only acts on moving charge, and is given by:                    F        ′            →        =      q    ′                      E        ′            →      In your example, we can take             v      →       along   x and             B      →       along z giving a                     F        y        ′            →       along   −      y    ′   so that the forces transform as :                    F        y        ′            →        =  γ                    F        →              y    ,        q    ′                      E        →              y    ′    =  γ  q            v      →        ×                    B        →              z  And this is consistent with how the fields should transform, remembering that charge is a relativistic invariant where   q  =      q    ′

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