*Addition of Velocities and Electromagnetic Interaction: Geometrical Derivations Using 3D Minkowski Diagrams*

Scientific Paper | |
---|---|

Title | Addition of Velocities and Electromagnetic Interaction: Geometrical Derivations Using 3D Minkowski Diagrams |

Read in full | Link to paper |

Author(s) | Calin Galeriu |

Keywords | classical electrodynamics, Minkowski space |

Published | 2003 |

Journal | Apeiron |

Volume | 10 |

Number | 1 |

No. of pages | 14 |

Pages | 1-14 |

**Read the full paper** here

## Abstract

This article presents intuitive, geometrical derivations of the relativistic addition of velocities, and of the elec-tromagnetic interaction between two uniformly moving charged particles, based on 2 spatial + 1 temporal dimensional Minkowski diagrams. We calculate the relativistic addition of velocities by projecting the world-line of the particle on the spatio-temporal planes of the reference frames considered. We calculate the real component of the electromagnetic 4-force, in the proper reference frame of the source particle, from the Coulomb force generated by a charged particle at rest. We then obtain the imaginary component of the 4-force, in the same reference frame, from the requirement that the 4-force be orthogonal to the 4-velocity. The 4-force is then projected on a real 3 dimensional space to give the Lorentz force.