How can magnetic field be a relativistic phenomenon?? According to Purcell (in his book: Electricity and Magnetism) the magnetic field force affecting a moving charge parallel to a current carrrying conductor is merely resulting from the electric field in the lab frame obtained when Lorentz transformation of the elecrtic field in the charge frame is done. If Magnetic phenomenon is a relativistic phenomenon, then we have to exclude the magnetic fields from the field transformation relations and keep only the electric field which say that the normal components of the electric field are related by gamma factor , while parallel components (to the direction of relative velocity between the 2 frames) are equal. This should be everything, But does this account for everything? Let's see... Consider two single charges in relative motion in two orhtogonal directions at the instant they were along the directions of one of the charges. In the lab frame, there are coulomb force in the radial direction, and Biot-Savart force in the normal directions direction. How can this Biot Savart force be derived from a relativistic effect like what Purcell did for the currents??