 





INDUCTION AND RELATIVITY:
In the field of electromagnetism, every point in space is characterized by two vector quantities, which determine the force on any charge. First, there is the electric force, which gives a force component independent of the motion of the charge, q. We describe it by the electric field, E . Second there is an additional force component, called the magnetic force, which depends on the relative velocity, v , of the charge in relation to reference frame of the magnetic field source.  The Lorentz Force Equation says that the force on an electric charge is dependent not only on where it is, but also on how fast it is moving in relation to something else, as in: 





We know from relativity that magnetism and electricity are not independent things  they should always be taken together as one complete electromagnetic field. Although in the static case Maxwell's equations separate into two distinct pairs, with no apparent connection between the two fields, nevertheless, in nature itself there is a very intimate relationship between them arising from the principle of relativity.
In accordance with Special Relativity, we must get the same physical result whether we analyze motion of a particle moving in a coordinate system at rest with respect to the magnetic source or at rest with respect to the particle. In the first instance the force was purely magnetic , in the second, it was purely electric . We know that a charge q is an invariant scalar quantity, independent of the frame of reference.
Since the F ' equal to F , we can calculate F ' as: 




Figure 2. A conducting rod is in relative motion with respect to a magnet. An observer S' fixed with respect to the rod, sees the magnet moving to the left. He also sees an electric force acting downward on the electron. 







Mathematically, it can be shown that a purely electric field in one reference frame can be magnetic in another. The separation of these interactions depends on which reference frame is chosen for description. In 1903  in a now famous experiment  Trouton and Noble showed that two electric charges moving with same constant velocity do not produce a magnetic interaction between themselves. This is consistent with the fundamental postulate of relativity. The force between two electric charges must be the same for an observer at rest with respect to the charges. This is true whether the charges move at constant velocity, or whether they remain fixed with respect with some reference frame.
Since electric and magnetic fields appear in different mixtures if we change our frame of reference, we must be careful about how we look at the fields E and B. We must not attach too much reality to them. The field lines may disappear if we try to observe them from different coordinate systems.
The field lines that we see in our textbooks for electric and magnetic fields are only mathematical constructs to help us understand and clarify the effects more easily. We can say more accurately that there is such a thing as a transformed electromagnetic field with a new magnitude and direction. Einstein's special relativity and Lorentz transformation make this view possible.



 
