Explicit definitions of electric and magnetic fields in potentials and derivation of Maxwell's equations

Based on the Lorentz force law given directly in terms of the scalar and the vector potentials, electric and magnetic fields are defined explicitly in terms of the potentials. These are in turn defined explicitly in terms of charge and current densities, respectively. The divergence and the curl relations of the two fields thus defined are just Maxwell's equations. The explicitness of the formulae provides a clearer way to understand the physical meanings of electric and magnetic fields.