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Magnetism in a current carrying wire

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If we use the right hand rule, we see that a hole current, or positive ion flow, creates a magnetic field around the wire where the flux moves in a clockwise direction. Counteractively, electron flow through a wire produces a magnetic flux that flows counterclockwise over the wire. Three questions:

1. Do I have this right?
2. Why on earth would a positive charge cause a circular flux in one direction whereas a negative charge cause one in the opposite direction? Is there some characteristic of the EM field that is responsible for this?
3. Do we get the same effect if the charges are flowing through free space and not a wire? Like cosmic rays or just shooting a beam of electrons through free space?

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