In conductors, the atoms contain so many electrons that the outermost ones can easily break away. When they break away they are free to move around if something forces them to move. These free electrons are the charges responsible for current in a conductor. Electric fields can put a force on a charge. This is described by the Lorentz force law. If that charge is free, it will move around. When there is a net flow of charge through a conductor, we call it an electrical current. Usually there is a voltage source that creates an electric field that puts a force on the charges near the source. These charges then push all the other charges through the conductor.
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