Magnetism is Just Electricity in Another Frame
Recently, I came across something that shook my whole understanding of electrodynamics. I had studied the different electric and magnetic fields their interactions and how one (quite mysteriously I might add) transforms to the other. A moving charge creates a magnetic field. A change in the magnetic field causes a current. Why do these different fields just change into each other based on the relative motion of their sources? The answer lies in special relativity. Rigorously of course, one could prove that the magnetic field is just the electric field in another reference frame using the relativistic transformation of the fields however, the setup that gave me intuition and helped build the idea is deriving the Biot Savart Law from special relativity. \[B = \frac{\mu_0I}{2\pi r} \] The setup Take an infinitely long wire, we aim to find the force on a moving charged particle adjacent to such a wire. Of course, the force is\[F = qv \times B\] But consider this, what causes the...
