A short analysis is made of some inconsistencies following from the introduction of Ohm's law into Maxwell's equations inside conductors because of its non-relativistic nature.To avoid these inconsistencies the law must be modified,in particular so that it takes into account the magnetic field;we show that this result can be obtained by using an elementary conduction model,avoiding the complications of the quantum-mechanical picture.The modified form of the law is used to obtain some results about the Hall effect and the limits of the concept of resistance.Finally,a further generalisation for non-isotropic and non-homogeneous conductors is outlined.

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