Explain the Lorentz transformation between two inertial frames. Obtain the transformation laws for the electric and magnetic fields.
The Lorentz transformation is a fundamental concept in classical electrodynamics and special relativity, describing how physical quantities change between two inertial frames moving at a constant velocity relative to each other. Consider two inertial frames, ( S ) and ( S' ), where ( S' ) moves with a velocity ( v ) along the x-axis relative to ( S ). The Lorentz transformation relates the spacetime coordinates ((t, x, y, z)) in frame ( S ) to ((t', x', y', z')) in frame ( S' ). The transformations are given by: [ t' = \gamma \left( ___ __________ __________ ______ _______.
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