Chapter 3: E and B Field Transformations
A pure electric field in one frame appears as a combination of electric and magnetic fields in another. This unification explains magnetism as a relativistic effect of moving charges.
Field Transformation Formulas
For a boost in the x-direction at velocity v:
Electric Field
\( E'_x = E_x \) (parallel unchanged)
\( E'_y = \gamma(E_y - vB_z) \)
\( E'_z = \gamma(E_z + vB_y) \)
Magnetic Field
\( B'_x = B_x \) (parallel unchanged)
\( B'_y = \gamma(B_y + vE_z/c^2) \)
\( B'_z = \gamma(B_z - vE_y/c^2) \)
Magnetism as a Relativistic Effect
Consider a current-carrying wire and a moving charge. In the wire's frame, there's only a magnetic force. In the charge's rest frame, length contraction changes charge densities, creating an electric force. Both give the same physical force—just different descriptions!
Key insight: Magnetism is electrostatics + special relativity. There's no independent magnetic phenomenon—just electric fields viewed from different frames.