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In other conductive materials, the electric current is due to the flow of both positively and negatively charged particles at the same time. In still others, the current is entirely due to positive charge flow. For example, the electric currents in electrolytes are flows of positively and negatively charged ions.
Actually, in some conductors the electric currents are a flow of genuinely positive charges, while in others the flows are indeed negative particles. And sometimes the currents are both positive and negative particles flowing at once, but in opposite directions within the same conductor. We cannot arbitrarily proclaim which way the charges flow, since their true direction always depends on the type of conductive material.