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We deduce the magnetic field produced by an infinite wire on a charge particle q that moves with velocity in a direction perpendicular to that of the wire. The wire carries an electric current I. We calculate the Lorentz force on the particle in the reference frame that travels with the particle; we then go back to the laboratory reference frame and determine the magnetic field.

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It is well known that a small number of graphene nanoparticles embedded in polymers enhance the electrical conductivity; the polymer changes from being an insulator to a conductor. The graphene nanoparticles induce several quantum effects, non-covalent interactions, so the percolation threshold is accelerated. We studied five of the most widely used polymers embedded with graphene nanoparticles: polystyrene, polyethylene-terephthalate, polyether-ketone, polypropylene, and polyurethane. The polymers with aromatic rings are affected mainly by the graphene nanoparticles due to the π-π stacking, and the long-range terms of the dispersion corrections are predominant. The polymers with linear structure have a CH-π stacking, and the short-range terms of the dispersion corrections are the important ones. We used the action radius as a measuring tool to quantify the non-covalent interactions. This action radius was the main parameter used in the Monte-Carlo simulation to obtain the conductivity at room temperature (300 K). The action radius was the key tool to describe how the percolation transition works from the fundamental quantum levels and connect the microscopic study with macroscopic properties. In the Monte-Carlo simulation, it was observed that the non-covalent interactions affect the electronic transmission, inducing a higher mean-free path that promotes the efficiency in the transmission.