Special relativity predicts that electric fields transform into magnetic fields via Lorentz transformations and that the vice versa also occurs. It also has been argued, since experiments verifying the quantum mechanical phenomenon of the Aharonov–Bohm effect, that the vector potentials are more fundamental than the field concepts.(adsbygoogle = window.adsbygoogle || []).push({});

Mathematically, how then does the magnetic field [itex]\mathbf{B} = \nabla \times \mathbf{A},[/itex] transform into an electric field [itex]\mathbf{E_A} = - \frac { \partial \mathbf{A} } { \partial t },[/itex] (or vice versa) in the case where the scalar potential is zero (thus [itex]- \nabla \phi=0[/itex])?

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# LT of the magnetic vector potential when the scalar potential=0

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