Geometrical meaning of Lorentz equation?

[eljose79]

Could we give a geometrical meaning of the Lorentz equation

mx´´=e(vxB)+eE...similar to that of gravitation..by considering that


e(vxB)+eE comes from a potential..and the electrons are moving in geodesics?..

 

[pmb]

Originally posted by eljose79
Could we give a geometrical meaning of the Lorentz equation

mx´´=e(vxB)+eE...similar to that of gravitation..by considering that


e(vxB)+eE comes from a potential..and the electrons are moving in geodesics?..

If the electron is moving in an EM field then it's not moving on a geodesic unless the force on the electron is zero. There are circumstances such that the electron is moving in an EM field and force free but not in general.

Pmb

 

[Graeme Robinson]

The Lorentz equation, also known as the Lorentz force law, describes the motion of a charged particle in an electromagnetic field. It states that the acceleration of the particle is equal to the sum of the electric and magnetic forces acting on it. This equation has a clear geometrical interpretation, similar to that of gravitation, when considering the motion of charged particles in an electromagnetic field.

The term e(vxB) represents the magnetic force, which is perpendicular to both the velocity of the particle and the magnetic field. This can be seen as a centripetal force, causing the particle to move in a circular path around the magnetic field lines. This is similar to the gravitational force, which also causes objects to move in a circular path around massive bodies.

The term eE represents the electric force, which is parallel to the electric field. This can be seen as a tangential force, causing the particle to accelerate in the direction of the electric field. This is similar to the gravitational force, which also causes objects to accelerate towards massive bodies.

By considering the electrons as moving in geodesics, we can also draw a parallel to the concept of spacetime curvature in general relativity. Just as massive objects curve the fabric of spacetime, causing objects to move along geodesic paths, charged particles moving in an electromagnetic field also experience a curvature in their trajectory. This curvature can be understood as the result of the combined electric and magnetic forces acting on the particle.

In summary, the Lorentz equation can indeed be given a geometrical interpretation by considering the motion of charged particles in an electromagnetic field. This interpretation is similar to that of gravitation, with the forces acting on the particle being analogous to centripetal and tangential forces, and the trajectory of the particle being affected by the curvature of spacetime.