Magnetic field around a wire
When a charged particle—such as an electron, proton or ion—is in motion, magnetic lines of force rotate around the particle. Since electrical current moving through a wire consists of electrons in motion, there is a magnetic field around the wire.
This field can be demonstrated by placing fine iron filings or shavings on a card and sticking a wire through the middle of the card. When a DC electrical current is passed through the wire, the iron filings align to show the magnetic field.
Right-hand rule for magnetic field
The right-hand rule for determining the direction of the magnetic field is that if you wrapped your right hand around a wire with your thumb pointing in the direction of the electrical current, then your fingers would be in the direction of the magnetic field.
You can verify the direction of the magnetic field by placing one or more compasses on a card and observing their direction.