In what direction is the magnetic field oriented about a conductor in relation to the direction of electron flow?

The direction of the magnetic field around a current-carrying wire is directly related to the direction of electron flow. To determine this orientation, physicists and engineers use the "left-hand rule" for electron flow. If you point the thumb of your left hand in the direction of the electron current (which flows from negative to positive), your fingers will naturally curl in the direction of the circular magnetic field lines that surround the conductor. Note that if you were using conventional current (which flows positive to negative), you would use the right-hand rule. Because the question specifically asks about "electron flow," the left-hand rule is the correct answer. The field forms circular loops around the wire, so it does not point parallel to the current.